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4. Quadratic Equations Class 10 Mathematics Solutions English Medium-Exercise 4.2
4. Quadratic Equations Class 10 Mathematics Solutions English Medium-Exercise 4.2 Get chapter-wise detailed explanations, step-by-step answers, important questions and exam-ready study material in Hindi and English medium.
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4. Quadratic Equations Class 10 Mathematics Solutions English Medium-Exercise 4.2
NCERT Solutions for Class 10 are specially prepared according to the latest CBSE syllabus (2026-27) to help students understand every concept clearly. These solutions provide step-by-step explanations, accurate answers, and exam-oriented guidance for all chapters. Class 10 students can improve their problem-solving skills, strengthen conceptual understanding, and prepare confidently for school as well as board examinations. All questions are solved in a simple and easy-to-understand language for both Hindi and English medium learners.
4. Quadratic Equations Class 10 Mathematics Solutions English Medium-Exercise 4.2
NCERT Solutions Class 10 Mathematics English Medium
4. Quadratic Equations
Topic: 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.
All Topics From 4. Quadratic Equations
See other sub-topics of this chapter:
1. Exercise 4.1 2. Exercise 4.2 3. Exercise 4.3 4. Exercise 4.4NCERT Solutions Class 10 Hindi and English Medium – Complete Study Material
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