quadratic equation word problems class 10 icse mcq

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MCQ Questions for Class 10 ICSE Maths Quadratic Equations (Online Available)

Free mcq test, table of content.

1. Ratio and Proportion

Quadratic Equations Test - 5

Duration: 19 Mins

Maximum Marks: 19

Read the following instructions carefully.

1. The test contains 19 total questions.

2. You have to finish the test in 19 minutes.

3. You will be awarded 1 mark for each correct answer.

4. There is no negative marking.

5. You can view your Score & Rank after submitting the test.

6. Check detailed Solution with explanation after submitting the test.

7. Rank is calculated on the basis of Marks Scored & Time

Quadratic Equations Test - 4

Duration: 15 Mins

Maximum Marks: 15

1. The test contains 15 total questions.

2. You have to finish the test in 15 minutes.

Quadratic Equations Test - 3

Duration: 10 Mins

Maximum Marks: 10

1. The test contains 10 total questions.

2. You have to finish the test in 10 minutes.

Quadratic Equations Test - 2

Quadratic equations test - 1.

The MCQ Questions for Class 10 ICSE Maths Quadratic Equations is one of the most important study materials which no student can afford to miss. Every student wants to ace their Maths final exam. Considering this problem, Selfstudys have developed the ICSE Quadratic Equations MCQ Questions for Class 10 to help the students grasp the concepts fastly and help them to do well in their exams.

The Class 10 ICSE Quadratic Equations MCQ Questions are created per the latest curriculum of ICSE (Indian Certificate of Secondary Examination). The student who regularly practises these Multiple Choice Questions will be able to practise important concepts in a well-explained manner which will help them score well on the exam. It also increases the conceptual knowledge of the student.

It is advisable for all the students to solve the ICSE Quadratic Equations MCQ Questions for Class 10 as it will increase their confidence and help them focus on the Maths Quadratic Equations topic properly.

About the MCQ Questions for Class 10 ICSE Maths Quadratic Equations

While practising the ICSE Quadratic Equations MCQ Questions for Class 10, all the students will get a chance to increase their knowledge and problem-solving skills. It helps the students to grasp the concepts in an easy way. Not only practise but Class 10 ICSE Quadratic Equations MCQ Questions can also be really helpful for all the students in terms of revision if a student has covered their entire syllabus and wants to find their strong areas and weak areas.

The highly qualified subject matter experts who have years of experience in the field of education have created the ICSE Quadratic Equations MCQ Questions for Class 10 after going through the pattern of last year's question papers.

Stress and anxiety are very common among students during exam days. Some Students also find it difficult to concentrate on their exams due to this. The MCQ Questions for Class 10 Maths ICSE Quadratic Equations give them the right status of their progress and also helps the students keep calm and relaxed.

How to Attempt MCQ Questions for Class 10 ICSE Maths Quadratic Equations?

To attempt the ICSE Quadratic Equations MCQ Questions for Class 10 the right way, students need to follow the following steps:

Go to the website of Selfstudys i.e. Selfstudys.com.

MCQ Questions for Class 10 ICSE Maths Quadratic Equations, MCQ Questions for Class 10 ICSE Quadratic Equations, ICSE MCQ Questions for Quadratic Equations Class 10, Class 10 ICSE MCQ Questions Quadratic Equations, Quadratic Equations MCQ Questions for Class 10 ICSE

Once the website will open, you need to scroll down a bit and find the option of ‘Free Study Materials. Now you need to find the option of ‘CISCE’, tap on the option of ‘MCQs Tests’,

Now you need to select the subject for which you want to attempt the Class 10 MCQ.
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Instructions to Solve ICSE Quadratic Equations MCQ Questions for Class 10

Before attempting the MCQ test, all the students are advised to read the instructions for Class 10 ICSE Quadratic Equations MCQ Questions to attempt them in the right way and not miss anything:

The total number of questions will be 10 in the MCQ Questions for Class 10 ICSE Maths Quadratic Equations.
Out of the 4 options given, only 1 will be correct.
The duration of the test will be short to ensure that the students get time for other study resources.
To ensure time management, the duration of the ICSE Quadratic Equations MCQ Questions for Class 10 will be ten minutes.
The student will be awarded 1 mark for each correct answer.
After attempting the test, the students can check the answers to MCQ Questions for Class 10 ICSE Maths Quadratic Equations.
The rank of the ICSE Quadratic Equations MCQ Questions for Class 10 will be given as per the scores which are secured by other students in the test and the time taken by them to complete it.
Students can also re-attempt the MCQ Questions of Class 10 ICSE Maths Quadratic Equations if they are not satisfied with their scores.

How to Prepare for the MCQ Questions of Class 10 ICSE Maths Quadratic Equations?

The MCQs are developed by our highly qualified subject matter experts to test the exam progress of a student. In the ICSE Quadratic Equations MCQ Questions for Class 10, out of 4 options, a student needs to select 1 option and 3 options will be incorrect. Some of the most important tips are:

Go through your notes: The first step includes going through your concept notes to grasp the concepts in an in-depth manner. Going through the notes and writing them in your own words can be highly beneficial for all the students in attempting the MCQ Questions for Class 10 ICSE Maths Quadratic Equations.
Start studying in advance: All the students who want to prepare for the MCQs in a proper way and want to score really well on their MCQ test must start studying in advance so that they are fully prepared for the exam. For example, a student can start studying days before the ICSE Quadratic Equations MCQ Questions for Class 10 online to create a strong base of all the concepts.
Make a plan for your exam strategy: In this tip, the students need to design the exam strategy for the answers that they do not know. One of the most common questions which students ask themselves during the time of exam is “whether they should skip the question or do guesswork?” While attempting the MCQ Questions for Class 10 ICSE Maths Quadratic Equations, you can randomly guess the answers without worrying because there is no negative marking for the incorrect answers.
Always take short snack breaks: All the students are advised to take short snack breaks for 15-20 minutes to keep the brain active when they are going through the notes of Quadratic Equations. Create a study schedule allowing you to take short snack breaks between study periods.

What Are the Benefits of MCQ Questions for Class 10 ICSE Maths Quadratic Equations?

Attempting the test MCQs is a great method through which students are tested on their skills. It is used by school teachers as it helps to test the knowledge of the students. But do you know apart from this, the MCQs have various benefits too? Below are the benefits of ICSE Quadratic Equations MCQ Questions for Class 10:

Increase the confidence of all the students: There is no denying the fact that these MCQ Questions for Class 10 ICSE Maths Quadratic Equations help to increase the confidence level of the students. As they feel that they are aware of most of the answers and will be able to achieve good marks in their exams.
Ensures Time Management among the students: Time management is a very important skill which no student can afford to miss as it helps to ensure the value of time and will never miss any questions in MCQ Questions for Class 10 ICSE Maths Quadratic Equations due to less time. Effective time management also ensures that the student is working with higher productivity.
Different Skills are improved: The Class 10 ICSE Quadratic Equations MCQ Questions not only help the students to do an effective exam preparation but also help to increase the different skills of the students which can be highly beneficial for them. These skills consist of deep thinking skills, observation skills and more.
Upgrades the level of the students: The ICSE Quadratic Equations MCQ Questions for Class 10 will consist of some hard questions as the highly qualified subject matter experts develop them. This will help the students to upgrade themselves and think accordingly which can increase the chances of students to score well in their exams.

How to Get 100% Marks in MCQ Questions for Class 10 ICSE Maths Quadratic Equations?

Do you really want to ace MCQ Questions for Class 10 ICSE Maths Quadratic Equations? There are a lot of tips which can improve your scores drastically. Some of them are:

Pay attention and go through the notes: The first and most important step is to pay attention during the time of lectures and go through the notes which you have developed during class as it will help you to attempt the ICSE Quadratic Equations MCQ Questions for Class 10. If you find any concept hard, you can approach your faculties to clear your doubts. Also, do not miss any classes as there is a strong chance that you might miss anything important from Quadratic Equations.
Make use of sense memory: Whether you know this fact or not, the human brain is great at connecting smell or sounds with memories. You can actually benefit from this! Wear a perfume while you are studying a particular topic and wear the same perfume again before your MCQ Questions for Class 10 ICSE Maths Quadratic Equations and you will notice it.
Answer the questions you know first: In Class 10 ICSE Quadratic Equations MCQ Questions, there will be questions which you can answer just by looking at them. Students are advised to go through the test to find the questions which they can attempt in one go.
Always revise your answers after selecting the option: After attempting the Class 10 ICSE Quadratic Equations MCQ Questions, you can go through the test once again and go through all the answers. There is a strong possibility that the question which you didn’t attempt before, now makes sense to you.

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Class 10 Maths MCQs
Chapter 4 Quadratic Equations

Class 10 Maths Chapter 4 Quadratic Equations MCQs

Class 10 Maths MCQs for Chapter 4 (Quadratic Equations) are available online here with answers. All these objective questions are prepared as per the latest CBSE syllabus (2022 – 2023) and NCERT guidelines. MCQs for Class 10 Maths Chapter 4 are prepared according to the new exam pattern. Solving these multiple-choice questions will help students to score good marks in the board exams, which they can verify with the help of detailed explanations given here. To get chapter-wise MCQs, click here . Also, find the PDF of MCQs to download here for free.

Class 10 Maths MCQs for Quadratic Equations

CBSE board has released the datasheet for the Class 10 Maths exam. It is advised for students to start revising the chapters, for the exam. Here, we have given multiple-choice questions for Chapter 4 quadratic equations, to help students to solve different types of questions, which could appear in the board exam. They can build their problem-solving capacity and boost their confidence level by practising the questions here. Get important questions for class 10 Maths here at BYJU’S.

Click here to download the PDF of additional MCQs for Practice on Quadratic equations, Chapter of Class 10 Maths along with answer key:

Download PDF

Students can also get access to Quadratic equations Class 10 Notes here.

Below are the MCQs for Quadratic Equations

1. Equation of (x+1) 2 -x 2 =0 has number of real roots equal to:

Answer: (a) 1

Explanation: (x+1) 2 -x 2 =0

X 2 +2x+1-x 2 = 0

Hence, there is one real root.

2. The roots of 100x 2 – 20x + 1 = 0 is:

(a) 1/20 and 1/20

(b) 1/10 and 1/20

(d) None of the above

Answer: (c) 1/10 and 1/10

Explanation: Given, 100x 2 – 20x + 1=0

100x 2 – 10x – 10x + 1 = 0

10x(10x – 1) -1(10x – 1) = 0

(10x – 1) 2 = 0

∴ (10x – 1) = 0 or (10x – 1) = 0

⇒x = 1/10 or x = 1/10

3. The sum of two numbers is 27 and product is 182. The numbers are:

(a) 12 and 13

(b) 13 and 14

(d) 13 and 24

Answer: (b) 13 and 14

Explanation: Let x is one number

Another number = 27 – x

Product of two numbers = 182

x(27 – x) = 182

⇒ x 2 – 27x – 182 = 0

⇒ x 2 – 13x – 14x + 182 = 0

⇒ x(x – 13) -14(x – 13) = 0

⇒ (x – 13)(x -14) = 0

⇒ x = 13 or x = 14

4. If ½ is a root of the quadratic equation x 2 -mx-5/4=0, then value of m is:

Answer: (b) -2

Explanation: Given x=½ as root of equation x 2 -mx-5/4=0.

(½) 2 – m(½) – 5/4 = 0

¼-m/2-5/4=0

5. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, the other two sides of the triangle are equal to:

(a) Base=10cm and Altitude=5cm

(b) Base=12cm and Altitude=5cm

(d) Base=12cm and Altitude=10cm

Answer: (b) Base=12cm and Altitude=5cm

Explanation: Let the base be x cm.

Altitude = (x – 7) cm

In a right triangle,

Base 2 + Altitude 2 = Hypotenuse 2 (From Pythagoras theorem)

∴ x 2 + (x – 7) 2 = 13 2

By solving the above equation, we get;

⇒ x = 12 or x = – 5

Since the side of the triangle cannot be negative.

Therefore, base = 12cm and altitude = 12-7 = 5cm

6. The roots of quadratic equation 2x 2 + x + 4 = 0 are:

(a) Positive and negative

(b) Both Positive

(d) No real roots

Answer: (d) No real roots

Explanation: 2x 2 + x + 4 = 0

⇒ 2x 2 + x = -4

Dividing the equation by 2, we get

⇒ x 2 + 1/2x = -2

⇒ x 2 + 2 × x × 1/4 = -2

By adding (1/4) 2 to both sides of the equation, we get

⇒ (x) 2 + 2 × x × 1/4 + (1/4) 2 = (1/4) 2 – 2

⇒ (x + 1/4) 2 = 1/16 – 2

⇒ (x + 1/4)2 = -31/16

The square root of negative number is imaginary, therefore, there is no real root for the given equation.

Answer: (b) 3

Explanation:

Hence, we can write, √(6+x) = x

x 2 -3x+2x-6=0

x(x-3)+2(x-3)=0

(x+2) (x-3) = 0

Since, x cannot be negative, therefore, x=3

8. The sum of the reciprocals of Rehman’s ages 3 years ago and 5 years from now is 1/3. The present age of Rehman is:

Answer: (a) 7

Explanation: Let, x is the present age of Rehman

Three years ago his age = x – 3

Five years later his age = x + 5

Given, the sum of the reciprocals of Rehman’s ages 3 years ago and after 5 years is equal to 1/3.

∴ 1/x-3 + 1/x-5 = 1/3

(x+5+x-3)/(x-3)(x+5) = 1/3

(2x+2)/(x-3)(x+5) = 1/3

⇒ 3(2x + 2) = (x-3)(x+5)

⇒ 6x + 6 = x 2 + 2x – 15

⇒ x 2 – 4x – 21 = 0

⇒ x 2 – 7x + 3x – 21 = 0

⇒ x(x – 7) + 3(x – 7) = 0

⇒ (x – 7)(x + 3) = 0

⇒ x = 7, -3

We know age cannot be negative, hence the answer is 7.

9. A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

(a) 30 km/hr

(b) 40 km/hr

(d) 60 km/hr

Answer: (b) 40 km/hr

Explanation: Let x km/hr be the speed of train.

Time required to cover 360 km = 360/x hr.

As per the question given,

⇒ (x + 5)(360-1/x) = 360

⇒ 360 – x + 1800-5/x = 360

⇒ x 2 + 5x + 10x – 1800 = 0

⇒ x(x + 45) -40(x + 45) = 0

⇒ (x + 45)(x – 40) = 0

⇒ x = 40, -45

Negative value is not considered for speed hence the answer is 40km/hr.

10. If one root of equation 4x 2 -2x+k-4=0 is reciprocal of the other. The value of k is:

Answer: (b) 8

Explanation: If one root is reciprocal of others, then the product of roots will be:

α x 1/α = (k-4)/4

11. Which one of the following is not a quadratic equation?

(a) (x + 2) 2 = 2(x + 3)

(b) x 2 + 3x = (–1) (1 – 3x) 2

(d) x 3 – x 2 + 2x + 1 = (x + 1) 3

Answer: (c) (x + 2) (x – 1) = x 2 – 2x – 3

We know that the degree of a quadratic equation is 2.

By verifying the options,

x 2 + 4x + 4 = 2x + 6

x 2 + 2x – 2 = 0

This is a quadratic equation.

x 2 + 3x = -1(1 + 9x 2 – 6x)

x 2 + 3x + 1 + 9x 2 – 6x = 0

10x 2 – 3x + 1 = 0

x 2 + x – 2 = x 2 – 2x – 3

x 2 + x – 2 – x 2 + 2x + 3 = 0

This is not a quadratic equation.

12. Which of the following equations has 2 as a root?

(a) x 2 – 4x + 5 = 0

(b) x 2 + 3x – 12 = 0

(d) 3x 2 – 6x – 2 = 0

Answer: (c) 2x 2 – 7x + 6 = 0

If 2 is a root then substituting the value 2 in place of x should satisfy the equation.

Let us verify the given options.

(a) x 2 – 4x + 5 = 0

(2) 2 – 4(2) + 5 = 1 ≠ 0

So, x = 2 is not a root of x 2 – 4x + 5 = 0

(2) 2 + 3(2) – 12 = -2 ≠ 0

So, x = 2 is not a root of x 2 + 3x – 12 = 0

2(2) 2 – 7(2) + 6 = 0

Here, x = 2 is a root of 2x 2 – 7x + 6 = 0

13. A quadratic equation ax 2 + bx + c = 0 has no real roots, if

(a) b 2 – 4ac > 0

(b) b 2 – 4ac = 0

(d) b 2 – ac < 0

Answer: (c) b 2 – 4ac < 0

A quadratic equation ax 2 + bx + c = 0 has no real roots, if b 2 – 4ac < 0. That means, the quadratic equation contains imaginary roots.

14. The product of two consecutive positive integers is 360. To find the integers, this can be represented in the form of quadratic equation as

(a) x 2 + x + 360 = 0

(b) x 2 + x – 360 = 0

(d) x 2 – 2x – 360 = 0

Answer: (b) x 2 + x – 360 = 0

Let x and (x + 1) be the two consecutive integers.

According to the given,

x(x + 1) = 360

x 2 + x = 360

x 2 + x – 360

15. The equation which has the sum of its roots as 3 is

(a) 2x 2 – 3x + 6 = 0

(b) –x 2 + 3x – 3 = 0

(d) 3x 2 – 3x + 3 = 0

Answer: (b) –x 2 + 3x – 3 = 0

The sum of the roots of a quadratic equation ax 2 + bx + c = 0, a ≠ 0 is given by,

Coefficient of x / coefficient of x 2 = –(b/a)

Let us verify the options.

(a) 2x 2 – 3x + 6 = 0

Sum of the roots = – b/a = -(-3/2) = 3/2

(b) -x 2 + 3x – 3 = 0

Sum of the roots = – b/a = -(3/-1) = 3

2x 2 – 3x + √2 = 0

Sum of the roots = – b/a = -(-3/3) = 1

16. The quadratic equation 2x 2 – √5x + 1 = 0 has

(a) two distinct real roots

(b) two equal real roots

(d) more than 2 real roots

Answer: (c) no real roots

2x 2 – √5x + 1 = 0

Comparing with the standard form of a quadratic equation,

a = 2, b = -√5, c = 1

b 2 – 4ac = (-√5) 2 – 4(2)(1)

= 5 – 8

= -3 < 0

Therefore, the given equation has no real roots.

17. The equation (x + 1) 2 – 2(x + 1) = 0 has

(a) two real roots

(b) no real roots

(d) two equal roots

Answer: (a) two real roots

(x + 1) 2 – 2(x + 1) = 0

x 2 + 1 + 2x – 2x – 2 = 0

x 2 – 1 = 0

18. The quadratic formula to find the roots of a quadratic equation ax 2 + bx + c = 0 is given by

(a) [-b ± √(b 2 -ac)]/2a

(b) [-b ± √(b 2 -2ac)]/a

(d) [-b ± √(b 2 -4ac)]/2a

Answer: (d) [-b ± √(b 2 -4ac)]/2a

The quadratic formula to find the roots of a quadratic equation ax 2 + bx + c = 0 is given by [-b ± √(b 2 -4ac)]/2a.

19. The quadratic equation x 2 + 7x – 60 has

(a) two equal roots

(b) two real and unequal roots

(b) no real roots

Answer: (b) two real and unequal roots

x 2 + 7x – 60 = 0

Comparing with the standard form,

a = 1, b = 7, c = -60

b 2 – 4ac = (7) 2 – 4(1)(-60) = 49 + 240 = 289 > 0

Therefore, the given quadratic equation has two real and unequal roots.

20. The maximum number of roots for a quadratic equation is equal to

Answer: (b) 2

The maximum number of roots for a quadratic equation is equal to 2 since the degree of a quadratic equation is 2.

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Quadratic Equations- Class X ICSE Mathematics MCQs

An equation with one variable in which the highest power of the variable is two is called a quadratic equation. The general form of the equation is a x² + b x + c = 0 where a, b, c ∈ R and a ≠ 0.

Click here to open MCQs of Quadratic Equations Solutions of the above MCQs are given below

Solutions

Question 1: The roots of 6 − 4 x²+5 x = 0 are

(a) − 2, −(3/4)
(b) 2, 3/4
(c) 2, −(3/4)
(d) none of these

Solution: 6 − 4 x² + 5 x = 0

⇒ 4 x² − 5 x − 6 = 0

⇒ 4 x² − 8 x + 3 x − 6 = 0

⇒ 4 x (x − 2) + 3 ( x − 2) = 0

⇒ (x – 2) (4 x + 3) = 0

∴ x = 2, −(3/4)

Question 2: The sum of two numbers is 9 and the sum of their

squares are 41. The numbers are

(a) 7, 2

Solution: Let the numbers be x and 9 − x.

∴ x² + (9 − x)² = 41

⇒ x² + 81 – 18 x + x² = 41

⇒ 2 x² −18 x + 40 = 0

⇒ x² − 9 x + 20 = 0

⇒ x² − 5 x − 4 x + 20 = 0

⇒ (x − 5) ( x − 4) = 0

∴ x = 5, 4 : If x = 5, other no 9 −5 = 4; if x = 4, other no = 5

the numbers are 5, 4

Question 3 : Which of the following is a quadratic equation?

(a) (x+4) (2x -1) = (2x+3) (x − 2)
(b) (x−1)³= x³ − 2 x²
(c) x(x+1) = (x+3) (x −3)
(d) (x −3)² +1 = x² + 2 x + 4

Solution: (a) (x+4) (2x −1) = (2 x + 3) (x − 2)

⇒ 2 x²+8x−x−4 = 2x² + 3x −4 x – 6

⇒ 8 x + 2 = 0 which is not a quadratic equation

(b) (x −1)³ = x³ − 2 x²

⇒ x³ − 3 x² + 3 x − 1 = x³ − 2 x²

⇒ x² − 3 x + 1 = 0 which is a quadratic equation

⇒ x² + x = x² − 9

⇒ x + 9 = 0 which is not a quadratic equation

(d) (x − 3)² + 1 = x² + 2 x + 4

⇒ x² − 6 x + 9 + 1 = x² + 2x + 4

⇒ 8 x − 6 = 0 which is not a quadratic equation

Question 4: If − (2/3) is a root of the equation

k x² − 13 x − 10 = 0, the value of k is

Solution: Putting k = −(2/3) in the equation k x² −13 x − 10 = 0

k (−2/3)² − 13 (−2/3) −10 = 0

⇒ k(4/9) + (26/3) – 10 = 0

⇒ k (4/9) = 10 − (26/3)

⇒ k (4/9) = 4/3 ⇒ k = 3

Question 5: The roots of the equation x² − 5 x + 6 = 0 are

(a) 6, −1
(b) −2, 3
(c) 1, −6
(d) 2, 3

Solution: x² – 5 x + 6 = 0

⇒ x² −2 x −3 x + 6 = 0

⇒ (x − 2) (x − 3) = 0

Question 6 : The solution of the equation 2 x² − 9 x + 10 = 0, x ∈ Z

(a) 2, (5/2)
(b) – 2, (5/2)
(d) (5/2)

Solution: 2 x² − 9 x + 10 = 0, x ∈ Z

⇒ 2 x² − 4 x −5 x + 10 = 0

⇒ 2 x (x − 2) − 5 ( x − 2) = 0

⇒ (x − 2) (2 x − 5) = 0

⇒ x = 2, (5/2) but x ∈ Z

Question 7: The solution of the quadratic equation x² – 3(x + 3) = 0

correct to two significant figures

(a) − 4.854, 1.854
(b) 4.85, −1.854
(c) 4.85, −1.85
(d) 4.9, − 1.9

Solution: x² − 3 (x + 3) = 0

⇒ x² − 3 x − 9 = 0

⇒ x = 4.9, − 1.9 (correct to two significant figures)

Question 8: The discriminant of the equation 4 x² − 5 x − 3 = 0 is

(d) none of these

Solution: Discriminant = (−5)²− 4 × 4 × (−3) = 25 + 48 = 73

Question 9: The quadratic equation 3 x² −4 √3 x + 4 = 0 has

(a) two distinct real roots
(b) two equal real roots
(c) no real roots
(d) two imaginary roots

Solution: Discriminant = (−4√3)² − 4 ×3×4 = 48 −48 = 0

Two roots are real and equal

Question 10: A trader bought a number of articles for ₹ 1200.

Ten were damaged and he sold each of the rest at ₹ 2 more than

what he paid for it, thus clearing a profit of ₹ 60 on the whole

transaction. The number of articles bought by the trader

Solution: 1st case: Let no of articles be x. ∴ original price of each article = ₹ (1200/x)

2nd case: No of articles = x − 10 and S.P = ₹ 1260 (net profit = ₹ 60)

Price of each article = ₹ {1260/(x −10) }

so the equation is 1260/(x −10) −(1200/x ) = 2

⇒ 60 x + 12000 = 2 x (x − 10)

⇒ 30 x + 6000 = x (x − 10)

⇒ x² − 10 x − 30 x − 6000 = 0

⇒ x² − 40 x − 6000 = 0

⇒ x² − 100 x + 60 x − 6000 = 0

⇒ x (x − 100) + 60 (x − 100) = 0

⇒ (x − 100) (x + 60) = 0

Question 11: The distance by road between two towns A and B is 216 km

and by rail, it is 208 km. A car travels at a speed of x km/h and the train

travels at a speed that is 16km/h faster than the car.

(i) the time taken by the car to reach town B from A in terms of x is

(a) (208/x) hr
(b) {216/(x+16)} hr
(c) (216/x) hr
(d) {208/(x+16)} hr

Solution: (216/x) hr

(ii) The time taken by the train to reach town B from A in terms of x is

(a) (208/x) h
(b) {216/(x+16)} h
(c) (216/x) h
(d) {208/(x+16)} h

Solution: {208/(x+16)} h

(iii) If the train takes 2 hours less than the car to reach town B,

then the quadratic equation formed is

(a) x² −12 x − 1728 = 0
(b) x² + 12 x + 1728 = 0
(c) x² −12 x + 1728 = 0
(c) x² + 12 x − 1728 = 0

Solution: (216/x) − (208/(x+16)) = 2

⇒ (216 x + 216 × 16 − 208 x) / (x (x +16)) = 2

⇒ 8 x + 216 × 16 = 2 (x² + 16 x)

⇒ 4 x + 216 × 8 = x² + 16 x

⇒ x² + 12 x − 1728 = 0

(iv) the speed of the car is

(a) 36 km/h
(b) 52 km/h
(c) 16 km/h
(d) 68 km/h

Solution: x² + 12 x – 1728 = 0

⇒ x² + 48 x − 36 x – 1728 = 0

⇒ x(x + 48) − 36(x + 48) = 0

⇒ (x + 48) ( x − 36) = 0

∴ x = − 48 (not possible) or x = 36

∴ the speed of the car is 36 km/h

Question 12: A two-digit number is such that the product of the

digits is 12. When 36 is added to this number the digits interchange

their places. Find the number.

Solution: Let the unit’s digit of the two-digit number be x. ∴ its ten’s digit = (12/x)

∴ the number is 10 × (12/x) + x = (120/x) +x

On interchanging the digits, the number = 10 x + (12/x)

According to question 10 x + (12/x) = (120/x) + x + 36

⇒ 9 x = (120/x) − (12/x) + 36

⇒ 9 x = (108/x) + 36

⇒ 9 x² = 108 + 36 x

⇒ x² = 12 + 4 x

⇒ x² − 4 x − 12 = 0

⇒ x² − 6 x + 2 x −12 = 0

⇒ x(x − 6) + 2(x −6) = 0

⇒ (x − 6) (x + 2)

⇒ x = 6 or x = −2 ( x being a digit of a number can’t be negative)

∴ unit digit = 6 and ten’s digit = 12/6 = 2.

Hence the number is 26

Question 13: At an annual function of the school, each student gives

a gift to every other student. If the number of gifts is 4830, find the

number of students.

Solution: Let the number of students be x.

∴ x (x −1) = 4830

⇒ x² − x − 4830 = 0

⇒ x² − 70 x + 69 x − 4830 = 0

⇒ x(x − 70) + 69(x − 70) = 0

⇒ (x − 70) ( x + 69) = 0

⇒ x = 70 or x = − 69 (number of students can’t be negative)

Hence number of students = 70

Question 14: If the perimeter of a rectangular plot is 32 m and the

length of its diagonal is 10 m, the area of the plot is

(a) 39 m²
(b) 78 m²
(c) 30 m²
(d) none of these

Solution: Let the length and breadth of the rectangle be x and y respectively.

∴ 2(x + y) = 32 ⇒ x + y = 16 ——— (i)

According to Pythagoras theorem, x² + y² = 10² ⇒ x² + y² = 100 ——- (ii)

squaring (i), x² + y² + 2 x y = 256

⇒ 100 + 2 x y = 256

⇒ 2 x y = 156

⇒ x y = 78

the area of the rectangle = length × breadth = x y = 78 m²

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MCQ Class 10 Physics

ISC / ICSE Board Paper

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Class 10 , ICSE Board Problems , Quadratic Equations (Advanced)

Class 10: Quadratic Equations – ICSE Board Problems

Hence, find the speed of the train. [1998]

$\displaystyle \text{Time taken by the car to reach town B from A } = \frac{216}{x}$

Given that the train takes 2 hours less than the car to reach town B

$\displaystyle \frac{216}{x} - \frac{208}{x+16} = 2$

Question 3: A hotel bill for the number of people for an overnight stay is Rs.4,800. If there were 4 people more, the bill each person had to pay, would have reduced by Rs.200. find the number of people staying overnight. [2000]

$\displaystyle = x$

Question 5: In an auditorium, seats were arranged in rows and columns. The number of rows was equal to the number of seats in each row. When the number of rows was doubled and the number of seats in each row was reduced by 10, the total number of seats increased by 300. Find The number of rows in the original arrangement. The number of seats in the auditorium after re-arrangement. [2003]

$\displaystyle (2x) \times (x-10) - x \times x = 300$

Question 7: A car covers a distance of 400 km at a certain speed. Had the speed been 12 km/h more, the time taken for the journey would have been 1 hour 40 minutes less. Find the original speed of the car. [2012]

$\displaystyle \text{ Therefore } \frac{400}{x} = \frac{400}{x+12} + \frac{100}{60}$

Question 9: By increasing the speed of the car by 10 km/hr, the time of the journey for a distance of 72 km is reduced by 36 minutes. Find the original speed of the car. [2005]

$\displaystyle \text{ Then the time taken to cover the distance } = \frac{72}{x}$

Hence given

$\displaystyle \frac{72}{x} - \frac{72}{x+10} = \frac{1}{2}$

Question 10: A two-digit number is such that the product of the digits is 6. When 9 is added to the number, the digits interchange their places. Find the number. [2014]

$\displaystyle xy$

Solving i) and ii)

$\displaystyle x(x+1) = 6$

Question 11: Five years ago, a woman’s age was square of her son’s age. 10 years hence her age will be twice that of her son. Find i) the age of her son five years ago ii) the present age of the woman. [2007]

$\displaystyle = x^2$

Question 12: A shopkeeper buys a certain number of books for Rs. 960. If the cost per book was Rs. 8 less, the number of books that he could have bought for Rs. 960 would be 4 more. Taking the original cost of each book to be x Rs. write an equation in x and solve for it. [2013]

$\displaystyle \text{ No of books bought } = \frac{960}{x}$

Question 13: Some students planned a picnic. The budget for the food was Rs. 480. As eight of the students failed to join the party, the cost of the food for each member increased by Rs. 10. Find how many students went for the picnic. [2008]

$\displaystyle = 480$

Simplifying

$\displaystyle x^2-8x-384 = 0$

4 thoughts on “ Class 10: Quadratic Equations – ICSE Board Problems ”

Add Comment

i would like to correct you that in the question no. 11 the equation will be 2(x+15)

I fixed it. Thank you for your contribution.

where are the questions from 2012 to 2020

I think you will find some of them them in the solved board question papers.

Let the original speed of train is x km/h Time taken to cover 63 km with speed x km/h, $Time = \frac {distance}{speed} =\frac { 63}{x}$ hours After 63 km, speed of train becomes(x + 6) km/h Time taken to cover 72km with speed (x + 6) km/h $Time = \frac {distance}{speed} =\frac { 72}{x +6}$ hours Now as per the question $\frac { 63}{x}+ \frac { 72}{x +6}= 3 $ $\frac { 21}{x}+ \frac { 24}{x +6}= 1$ $ \frac {(21x + 126 + 24x) }{x(x+6}= 1$ $45x + 126 = x^2+ 6x$ $x^2- 39x - 126 = 0$ (x + 3)(x - 42) = 0 ∴x = 42 and -3 , but x ≠ -3 as speed cannot be negative Hence, original speed of train = 42 km/h

Let n and n-2 be the two consecutive negative even integers then $n(n-2)=24$ $n^2 -2n-24=0$ or $(n-6)(n+4) =0$ n=6 or -4 Since we want the negative integers only, n=-4 other number =n-2= -4-2 = -6 So numbers are (-6,-4)

Let x= the length of the rectangle and y= its width As per the question $x = 3y- 2$ Given ,The area of this rectangle is 16 Now $Area =xy = 16 $ or $ (3y-2)y=16$ $3y^2- 2y- 16=0$ Factoring $ (3y-8)(y+2)=0$ y = 8/3 and -2 Since we can't have a negative width, y= 8/3 Now x=3y-2 = 6 Perimeter = 2x + 2y = 12 + 16/3 = 64/3

Let x be the smaller number x+2 could be the larger number $x(x+2)=224$ $x^2+2x-224=0$ Factoring the quadratics $(x+16)(x-14)=0$ x= -16 or 14 For positive Numbers x= 14 Second number= x+2= 16 So the numbers are 14 and 16 For Negative Numbers x=-16 Second number= x+2= -14 So the numbers are -16 and -14

Let p and q are days required for X and Y to complete the project alone Now p =q-5 Also $\frac {1}{p} + \frac {1}{q} = \frac {1}{6}$ or $\frac {1}{q-5} + \frac {1}{q} = \frac {1}{6}$ $\frac { q + q-5}{q(q-5)} = \frac {1}{6}$ $ 6(2q-5) = q^2 -5q$ $q^2 -17q +30=0$ factoring this quadratics q=15 or 2 It can not be 2 as then p will be negative So q=15 days and p=10 days

Let the speed of the stream be x km/hr. Distance upstream = Distance downstream = 24 km Speed of the boat going upstream=18 - x Speed of the boat going downstream=18+x Time taken going upstream = 24/18-x Time taken going downstream = 24/18+x Now as per question $ \frac {24}{18-x} = 1 + \frac {24}{18+x}$ $\frac {24}{18-x} = \frac {42+x}{18+x}$ $24(18+x) = (42+x) (18-x)$ $x^2 + 48x-182=0$ x=-54 or 6 Rejecting negative value, the speed of stream is 6 km/hr

let x be the base ,the altitude will be x-7 Now as per pythagorus theorem $x^2 +(x-7)^2 = 13^2$ $x^2 -7x -69=0$ x=12 or -5 Since x cannot be negative x=12

$kx(x-2 \sqrt {5}) + 10 =0$ $kx(x-2 \sqrt {5}) + 10 =0$ or $kx^2 -2 \sqrt {5} kx +10 =0$ For equal roots, Discriminant should be zero $b^2 -4ac=0$ here $b= -2 \sqrt {5} k$, a=k ,c=10 $( -2 \sqrt {5} k)^2 -4 \times k \times 10=0$ $20k^2 -40k=0$ or k=0 or 2 k cannot be zero, So correct value of k=2

Let denominator be x ,the numerator x-3. Fraction will be = $\frac {x-3}{x}$ Now when 2 is added New fraction= $\frac {x-3+2}{x+2}=\frac {x-1}{x+2} $ According to the question $\frac {x-3}{x} +\frac {x-1}{x+2}= \frac {29}{20}$ $ \frac {(x-3)(x+2) + x(x-1)}{x(x+2)} =\frac {29}{20}$ $\frac {2x^2 -2x-6}{x(x+2)} =\frac {29}{20}$ $20(2x^2 -2x-6) = 29x(x+2)$ $40x^2 -40x -120 =29x^2 + 58x$ $11x^2 -98x -120=0$ Factoring the quadratics x=10 or -12/11 So fraction is$\frac {x-3}{x} = \frac {7}{10}$

Let x and y hour be the time taken by larger pipe and smaller pipe to fill the swimming pool Now it is given $y - x = 10$ or $y = x + 10$ If smaller pipe takes x hours to fill the pool, it will fill 1/x part in 1 hour SimilaryIf larger pipe takes y hours to fill the pool, it will fill 1/y part in 1 hour According to question $ 4 \times \frac {1}{x} + 9 \times \frac {1}{y} = \frac {1}{2}$ or $ \frac {4}{x} + \frac {9}{y} = \frac {1}{2}$ Now putting y = x + 10 in this $ \frac {4}{x} + \frac {9}{x+10} = \frac {1}{2}$ $ \frac {4x+ 40 + 9x}{x(x+10)} = \frac {1}{2}$ $26x + 80 =x^2+10x$ $ x^2 - 16x - 80 = 0$ OR (x -20)(x+4) = 0 Neglecting negative root, x = 20 h And y = 30 h

Let x be the number,then $5x= 2x^2 -3$ $2x^2 -5x-3=0$ $2x^2 -6x + x-3=0$ $2x(x-3) + 1(x-3)=0$ or (2x+1)(x-3)=0 or x=3 as x is a positive integer

For an equation to have real roots, its discriminant should be greater than or equal to 0. $D=b^2 -4ac \geq 0$ For equation (1) $x^2+2px+64=0$ $ (2p)^2- 4 \times 64 \geq 0$ $ p�\geq 64 $ $ p\geq 8$ or $p \leq -8$ For equation (2) $x^2-8x+2p=0$ $64 -8p \geq0$ $8 \geq p$ Answer is $( -\infty , -8) \cup {8}$

Let age of zeba be x years As per the question $ (x-5)^2=11+5x $ $x^2+25-10x=11+5x$ $x^2-15x+14=0 $ $x^2-14x-x+14=0$ $(x-1)(x-14) So Zeba age will be 14 yrs because if she was 1 year old the 5 years younger cannot happen

Let x and x+7 are the two consecutive multiples of 7 Now as per question $x^2 + (x+7)^2 =637$ $x^2 + x^2 + 49 + 14x =637$ $x^2 + 7x -294=0$ x=-21 and 14 So answer is -21,-14 or 14,17

This Quadratic Word Problems Worksheet with Answers Class 10 Maths is prepared keeping in mind the latest syllabus of CBSE . This has been designed in a way to improve the academic performance of the students. If you find mistakes , please do provide the feedback on the mail.You can also download through below link Download Quadratic Word problems worksheet as pdf

Quadratic Polynomial
Factoring quadratics equations
Solving quadratic equations by completing the square
Solving quadratic equations by using Quadratic formula
How to solve Quadratic word problems
Quadratic Equation Cheat sheet
class 10 quadratic equations extra questions
Quadratic word problems Worksheet
Quadratic formula worksheet
NCERT Solutions Quadratic Equation Exercise 4.2
NCERT Solutions Quadratic Equation Exercise 4.3
NCERT Solutions Quadratic Equation Exercise 4.4

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ICSE Class 10 Maths Previous Years Questions Chapter-Quadratic Equations

One of the most important ways to prepare for the Board exams is by practicing the previous year papers. At our website, students can easily access the ICSE Class 10 Maths Previous Years Questions with solutions from 2010 to 2023. Scoring well in ICSE class 10 Math exam requires students to have a good understanding of the concepts and formulas. By solving these PYQs, students can get familiarized with the exam pattern and the types of questions asked in the exam. This can help them to approach the exam with confidence and reduce exam pressure.

ICSE Class 10 Maths Previous Years Questions with Solutions Chapter Quadratic Equations 2010 to 2023

The past year questions from Quadratic Equations available on our website are from the years 2023, 2022, 2020, 2019, 2018, 2017, 2016, 2015, 2014, 2013, 2012, 2011 and 2010. Each sum is solved in detail that helps students understand the marking pattern.

Moreover, practicing the ICSE Class 10 Maths Previous Years Questions Chapter- Quadratic Equations can be particularly beneficial for students. Quadratic Equations is an important topic in Maths and requires a good understanding of formulas and concepts. By practicing the ICSE Class 10 Maths previous years questions related to Quadratic Equations students can get a good grasp of the topic and be better prepared for the exam.

Q1. Solve the following quadratic equation: x 2 + 4x – 8 = 0

Give your answer correct to one decimal place. (Use mathematical tables if necessary.) [2023]

Answer: x= 1.5, -5.5

Step-by-step explanation:

Q2. If 3 is a root of the quadratic equation x 2 – px + 3 = 0 then p is equal to:

(d) 2 [2023]

Answer: (a) 4

Q3. One of the roots of the quadratic equation x 2 – 8x + 5 = 0 is 7.3166. The root of the equation correct to 4 significant figures is: [1]

(d) 7.32 [2021 Semester-1]

Answer: (b) 7.317

Q4. Which of the following quadratic equations has 2 and 3 as its roots? [1]

(a) x 2 – 5x + 6 =0

(b) x 2 + 5x + 6 = 0

(d) x 2 + 5x -6 =0 [2021 Semester-1]

Answer: (a) x 2 -5x+6=0

Step-by-step Explanation:

Q5. Solve the following Quadratic Equation:

𝑥 2 − 7𝑥 + 3 = 0 Give your answer correct to two decimal places. [2020]

Answer: x = 6.54 , 0.46

Q6. Solve for x the quadratic equation x 2 – 4x – 8 = 0

Give your answer correct to three significant figures. [2019]

Answer: x= 5.46 , -1.46

You can see video solution of these questions here .

Q7. Solve x 2 + 7x = 7 and give your answer correct to two decimal places. [4] [2018]

Answer: 0.89 , -7.89

Q8. Find the value of k for which the following equation has equal roots. [3]

x 2 + 4kx + (k 2 – k + 2) =0 [2018]

Answer: k= -1 or 2/3

Q9. Solve the equation 4x 2 – 5x – 3 = 0 and give your answer correct to two decimal places. [4] [2017]

Answer: x = 1.69 , -0.44

Q10. Solve the quadratic equation x 2 – 3(x + 3) = 0; Give your answer correct to two significant figures. [3] [2016]

Answer: x = 5.9 , -0.85

You can find ICSE Class 10 Maths Previous Years Questions with solution of each Chapter here .

Q11. Find the value of ‘K’ for which x = 3 is a solution of the quadratic equation, (K + 2) x 2 – Kx + 6 = 0.Thus find the other root of the equation. [2015]

Answer: k= -4, other root = -1

Q12. Solve for x using the quadratic formula. Write your answer correct to two significant figures,

(x – 1) 2 – 3x + 4 = 0. [3] [2014]

Answer: 3.6 , 1.4

Q13. Solve the following equation and calculate the answer correct to two decimal places:

x 2 – 5x – 10 = 0 [3] [2013]

Answer: 6.53 , -1.53

Q14. Without solving the following quadratic equation, find the value of ‘p’ for which the given equation has real and equal roots: x 2 + (p – 3)x + p = 0 [2013]

Answer: p= 1 or 9

Q15. Without solving the following quadratic equation, find the value of ‘m’ for which the given equation has real and equal roots.

x 2 + 2 (m – 1) x + (m + 5) = 0 [3] [2012]

Answer: m = -1 , 4

Q16. Solve the following equation and give your answer correct to 3 significant figures:

5x 2 – 3x – 4 = 0 [3] [2012]

Answer: 1.24 , -0.643

Q17. Solve the following equation:

Give your answer correct to two significant figures. [3] [2011]

Answer: 8.2 , -2.2

Q18. Without solving the following quadratic equation, find the value of ‘p’ for which the roots are equal. px 2 – 4x + 3 = 0 [3] [2010]

Answer: p = 4/3

Q19. A man covers a distance of 100 km, travelling with a uniform speed of x km/hr. Had the speed been 5 km/hr more it would have taken 1 hour less. Find x the original speed. [2023]

Answer: 20 km/h

Original speed = x km/hr

Distance = 100 km

Therefore, Time taken = 100/x hr

Now, if speed = (x+5) km/hr

Then, by the problem,

Q20. The difference of two natural numbers is 7 and their product is 450. Find the numbers. [2020]

Answer: 18 and 25

Let the two numbers be x and (x-7).

by the problem,

x(x-7) = 450

or, x 2 – 7x – 450 = 0

or, x 2 – 25x + 18x – 450 = 0

or, x(x – 25) + 18(x – 25) = 0

or, (x – 25)(x + 18) = 0

Either (x – 25) = 0 or (x + 18) = 0

x = 25 or -18

As natural numbers cannot be negative, therefore

One number is 25 and

the other number is (25-7) = 18.

Q21. The product of two consecutive natural numbers which are multiples of 3 is equal to 810. Find the two numbers. [3] [2019]

Answer: 27 and 30

Let the two numbers be 3x and 3(x+1).

You can see video solutions to these questions here .

Q22. ₹ 7500 were divided equally among a certain number of children. Had there been 20 less children, each would have received ₹ 100 more. Find the original number of children. [2018]

Q23. Two cars X and Y use 1 litre of diesel to travel x km and (x + 3) km respectively. If both the cars covered a distance of 72 km, then:

i. The number of litres of diesel used by car X is: [1]

ii. The number of litres of diesel used by car Y is: [1]

iii. If car X used 4 litres of diesel more than car Y in the journey, then: [1]

iv. The amount of diesel used by the car X is: [1] (a) 6 litres

(b) 12 litres

(d) 24 litres [2021 Semester-1]

Answer: i. (c) , ii. (b) , iii. (c) , iv. (b)

Q24. The sum of the ages of Vivek and his younger brother Amit is 47 years. The product of their ages in years is 550. Find their ages. [4] [2017]

Answer: 25 years, 22 years

Let the age of Vivek be x years and that of his younger brother be (47-x) years.

By the problem,

x(47 – x) = 550

or, 47x – x 2 =550

or, x 2 – 47x + 550 = 0

or, x 2 – 25x – 22x + 550 = 0

or, x(x – 25) – 22(x – 25) = 0

or, (x – 25)(x – 22) = 0

either (x – 25) = 0 or (x – 22) = 0

x = 25 or 22

Therefore, Vivek’s age is 25 years and his younger brother’s age is 22 years.

Q25. A bus covers a distance of 240 km at a uniform speed. Due to heavy rain its speed gets reduced by 10 km/h and as such it takes two hours longer to cover the total distance. Assuming the uniform speed to be ‘x’ km/h, form an equation and solve it to evaluate ‘x’. [3] [2016]

Answer: 40 km/h

Q26. Sum of two natural numbers is 8 and the difference of their reciprocal is 2 / 15. Find the numbers. [3] [2015]

Answer: 3 and 5

Let the two natural numbers be x and (8-x).

Now, by the problem,

Q27. A two digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number. [4] [2014]

Q28. A shopkeeper purchases a certain number of books for Rs. 960. If the cost per book was 8 less, the number of books that could be purchased for Rs. 960 would be 4 more. Write an equation, taking the original cost of each book to be Rs. x, and solve it to find the original cost of the books.[4] [2013]

Answer: Rs. 48

Q29. A car covers a distance of 400 km at a certain speed. Had the speed been 12 km/h more, the time taken for the journey would have been 1 hour 40 minutes less. Find the original speed of the car. [4] [2012]

Answer: 48 km/h

Q30. Rs.480 is divided equally among ‘x’ children. If the number of children was 20 more, then each would have got Rs. 12 less. Find ‘x’. [3] [2011]

Q31. A positive number is divided into two parts such that the sum of the squares of the two parts is 20. The square of the larger part is 8 times the smaller part. Taking x as the smaller part of the two parts, find the number. [4] [2010]

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Quadratic Equation Class 10 Maths ICSE Solutions

Get ICSE Solutions for Class 10 Mathematics Chapter 6 Quadratic Equation for ICSE Board Examinations on ICSESolutions.com. We provide step by step Solutions for ICSE Mathematics Class 10 Solutions Pdf. You can download the Class 10 Maths ICSE Textbook Solutions with Free PDF download option.

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Download Formulae Handbook For ICSE Class 9 and 10

The standard form of a quadratic equation is ax 2 + bx + c = 0, where a, b and c are all real numbers and a ≠ 0. e.g., equation 4x 2 + 5x – 6 = 0 is a quadratic equation in standard form.
Every quadratic equation gives two values of the unknown variable and these values are called roots of the equation.

To examine the nature of the roots: Examining the roots of a quadratic equation means to see the type of its roots i.e., whether they are real or imaginary, rational or irrational, equal or unequal. The nature of the roots of a quadratic equation depends entirely on the value of its discriminant b 2 – 4ac. Case I: If a, b and c are real numbers and a ≠ 0, then discriminant: (i) b 2 – 4ac = 0 ⇒ the roots are real and equal. (ii) b 2 – 4a c > 0 ⇒ the roots are real and unequal. (iii) b 2 – 4ac < 0 ⇒ the roots are imaginary (not real). Case II: If a, b and c are rational numbers and a ≠ 0, then discriminant. (i) b 2 – 4ac = 0 ⇒ the roots are rational and equal. (ii) b 2 – 4ac > 0 and b 2 – 4ac is a perfect square ⇒ the roots are rational and unequal. (iii) b 2 – 4ac > 0 and b 2 – 4ac is not a perfect square ⇒ the roots are irrational and unequal. (iv) b 2 – 4ac < 0 ⇒ the roots are imaginary.

Determine the Following

Question 57. Car A travels x km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol. (i) Write down the number of litres of petrol used by car A and car B in covering a distance of 400 km. (ii) If car A use 4 litre of petrol more than car B in covering the 400 km, write down and equation in x and solve it to determine the number of litre of petrol used by car B for the journey.