NCERT SOLUTIONS FOR CLASS 10 MATHS CHAPTER 4 QUADRATIC EQUATIONS EX 4.2
Question 1. Find the roots of the following quadratic equations by factorisation:
(i) x2 -3x – 10 = 0
(ii) 2x2 + x – 6 = 0
(iii) √2x2 + 7x + 5√2 = 0
(iv) 2x2 – x + 1/ 8 = 0
(v) 100 x2 – 20x + 1 = 0
Solution:
![NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Exercise 4.2 Q1](https://www.learncbse.in/wp-content/uploads/2018/11/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-Exercise-4.2-Q1.png)
![NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Exercise 4.2 Q1.1](https://www.learncbse.in/wp-content/uploads/2018/11/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-Exercise-4.2-Q1.1.png)
![NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Exercise PDF 4.2 Q1](https://www.learncbse.in/wp-content/uploads/2018/11/NCERT-Solutions-for-Class-10-Maths-Chapter-4-Quadratic-Equations-Exercise-PDF-4.2-Q1.png)
Question 2. Solve the following situations mathematically:
(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.
Solution:
(i) Let us say, the number of marbles John has = x.
Therefore, the number of marble Jivanti have = 45 – x
After losing 5 marbles each,
Number of marbles John have = x – 5
Number of marble Jivanti have = 45 – x – 5 = 40 – x
Given that the product of their marbles is 124.
∴ (x – 5)(40 – x) = 124
⇒ x2 – 45x + 324 = 0
⇒ x2 – 36x – 9x + 324 = 0
⇒ x(x – 36) – 9(x – 36) = 0
⇒ (x – 36) (x – 9) = 0
Thus, we can say,
x – 36 = 0 or x – 9 = 0
⇒ x = 36 or x = 9
Therefore,
If, John’s marbles = 36,
Then, Jivanti’s marbles = 45 – 36 = 9
And if John’s marbles = 9,
Then, Jivanti’s marbles = 45 – 9 = 36
(ii) Let us say, number of toys produced in a day be x.
Therefore, cost of production of each toy = Rs(55 – x)
Given, total cost of production of the toys = Rs 750
∴ x(55 – x) = 750
⇒ x2 – 55x + 750 = 0
⇒ x2 – 25x – 30x + 750 = 0
⇒ x(x – 25) – 30(x – 25) = 0
⇒ (x – 25)(x – 30) = 0
Thus, either x – 25 = 0 or x – 30 = 0
⇒ x = 25 or x = 30
Hence, the number of toys produced in a day, will be either 25 or 30.
Question 3. Find two numbers whose sum is 27 and the product is 182.
Solution:
![Exercise 4.2 Class 10 Maths NCERT Solutions Chapter 4 Quadratic Equations Free PDF Download Q3](https://www.learncbse.in/wp-content/uploads/2018/11/Exercise-4.2-Class-10-Maths-NCERT-Solutions-Chapter-4-Quadratic-Equations-Free-PDF-Download-Q3.png)
Question 4.
Find two consecutive positive integers, the sum of whose squares is 365.
Solution: Let the two consecutive integers be x and x + 1.
According to question,
![](https://cbseinsights.com/wp-content/uploads/2021/06/image-137.png)
![](https://cbseinsights.com/wp-content/uploads/2021/06/image-138.png)
Hence, the two consecutive positive integers are 13 and 13 + 1 = 14.
Question 5.
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
Solution:
![Exercise 4.2 Class 10 Maths NCERT Solutions Chapter 4 Quadratic Equations Q5](https://www.learncbse.in/wp-content/uploads/2018/11/Exercise-4.2-Class-10-Maths-NCERT-Solutions-Chapter-4-Quadratic-Equations-Q5.png)
Question 6.
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 ₹90, find the number of articles produced and the cost of each article.
Solution:
Let the total number of pottery articles produced in a day = x
Cost of production of each article = Rs 90 / x
According to question,
![](https://cbseinsights.com/wp-content/uploads/2021/06/image-139-1024x273.png)
![](https://cbseinsights.com/wp-content/uploads/2021/06/image-140.png)