## Chapter 4 Quadratic Equations Ex 4.2

**Question 1.** **Find the roots of the following quadratic equations by factorisation:** **(i) x ^{2} -3x – 10 = 0**

**(ii) 2x**

^{2}+ x – 6 = 0**(iii) √2x**

^{2}+ 7x + 5√2 = 0**(iv) 2x**18

^{2}– x +**= 0 8**

**(v) 100 x**

^{2}– 20 X + 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 ₹750. We would like to find out the number of toys produced on that day. **Solution:(i)** Let the number of marbles John had be x

Then, the number of marbles Jivanti had = 45 -x

The number of marbles left with John, when he lost 5 marbles = x – 5

The number of marbles left with Jivanti, when she lost 5 marbles = 45 -x – 5 = 40 -x

**Question 3.Find two numbers whose sum is 27 and product is 182.**

**Solution:**

Let one number = x ,

∴ other number = 21 -x

According to question,

**Question 4.Find two consecutive positive integers, sum of whose squares is 365.**

**Solution:**

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

According to question,

**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:**

Let base = x cm,

∴ height = (x – 7) cm

By Pythagoras Theorem,

(base)² + (height)² = (hypotenuse)²

**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:**