NCERT SOLUTIONS FOR CLASS 10 MATHS CHAPTER 4 QUADRATIC EQUATIONS EX 4.2

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:

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:

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,

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:

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,