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4. Quadratic Equations Mathematics class 10 in English Medium ncert book solutions Exercise 4.2
4. Quadratic Equations Exercise 4.2 – Complete NCERT Book Solutions for Class 10 Mathematics (English Medium). Get all chapter explanations, extra questions, solved examples and additional practice questions for 4. Quadratic Equations Exercise 4.2 to help you master concepts and score higher.
4. Quadratic Equations Mathematics class 10 in English Medium ncert book solutions Exercise 4.2
NCERT Solutions for Class 10 Mathematics play an important role in helping students understand the concepts of the chapter 4. Quadratic Equations clearly. This chapter includes the topic Exercise 4.2 , which is essential from both academic and examination point of view. The solutions provided here are prepared strictly according to the latest NCERT syllabus and follow the guidelines of CBSE to ensure accuracy and relevance. Each question is explained in a simple and student-friendly manner so that learners can grasp the concepts without confusion. These NCERT Solutions are useful for regular study, homework help, and exam preparation. All textbook questions are solved step by step to improve problem-solving skills and conceptual clarity. Students of Class 10 studying Mathematics can use these solutions to revise important topics, understand difficult questions, and practise effectively before examinations. The chapter 4. Quadratic Equations is explained in a structured way, making it easier for students to connect the theory with the topic Exercise 4.2 . By studying these updated NCERT Solutions for Class 10 Mathematics, students can build a strong foundation, boost their confidence, and score better marks in school and board exams.
4. Quadratic Equations
Exercise 4.2
Exercise: 4.2
Q1. Find the roots of the following quadratic equations by factorisation:
(i) x2 - 3x - 10 = 0,
Solution:
x2 - 3x - 10 = 0
⇒x2 - 5x + 2x - 10 = 0
⇒ x( x - 5 ) + 2(x - 5) = 0
⇒( x - 5 ) (x + 2) = 0
⇒( x - 5 ) = 0, (x + 2) = 0
|
x - 5 = 0 x = 5 |
x + 2 = 0 x = - 2 |
(ii) 2x2 + x - 6 = 0;
Solution:
⇒2x2 + 4x - 3x - 6 = 0
⇒ 2x( x + 2 ) - 3(x + 2) = 0
⇒( x + 2 ) (2x - 3) = 0
⇒( x + 2 ) = 0, (2x - 3) = 0
|
x + 2 = 0 x = - 2 |
2x - 3 = 0 2x = 3
|
(iii) √2x2 + 7x + 5√2 = 0;
Solution:
√2x + 2x + 5x + 5√2 = 0√2x(x + √2) + 5(x + √2) = 0
(x + √2) (√2x + 5) = 0;(x + √2) = 0, (√2x + 5) = 0
x = - √2, √2x = - 5
x = - 5/√2
x = -5√2/2
(iv) 2x2 - x + 1/8 =0
Solution:
| 2x2 - x + | 1 | = 0 |
| 8 |
Or ⇒16x2 - 8x + 1 = 0;
⇒16x2 - 4x - 4x + 1 = 0
⇒ 4x( 4x - 1 ) - 1(4x - 1) = 0
⇒( 4x - 1 ) (4x - 1) = 0
⇒( 4x - 1 ) = 0, (4x - 1) = 0
|
4x - 1 = 0 4x = 1
|
4x - 1 = 0 4x = 1
|
(v) 100x2 - 20x + 1 = 0;
Solution:
100x2 - 20x + 1 = 0⇒100x2 - 10x - 10x + 1 = 0
⇒ 10x( 10x - 1 ) - 1(10x - 1) = 0
⇒( 10x - 1 ) (10x - 1) = 0
⇒( 10x - 1 ) = 0, (10x - 1) = 0
|
10x - 1 = 0 10x = 1
|
10x - 1 = 0 10x = 1
|
Q2. Solve the problems given in Example 1.
Example1:
(i) John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with.
(ii) A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. We would like to find out the number of toys produced on that day.
Q3. Find two numbers whose sum is 27 and product is 182.
Q4. Find two consecutive positive integers, sum of whose squares is 365.
Q5. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.Q6. A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article.
See other sub-topics of this chapter:
1. Exercise 4.1 2. Exercise 4.2 3. Exercise 4.3 4. Exercise 4.4