NCERT Solutions
Class 10 - Mathematics - Chapter 4: QUADRATIC EQUATIONS

Exercise 4.2

Find the roots of the following quadratic equations by factorisation:

(i) \(x^2 - 3x - 10 = 0\)

(ii) \(2x^2 + x - 6 = 0\)

(iii) \(\sqrt{2}x^2 + 7x + 5\sqrt{2} = 0\)

(iv) \(2x^2 - x + \dfrac{1}{8} = 0\)

(v) \(100x^2 - 20x + 1 = 0\)

Solve the problems given in Example 1.

Example 1: Represent the following situations mathematically and solve them:

(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. How many marbles did each of them have originally?

(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. How many toys were produced on that day?

Find two numbers whose sum is 27 and product is 182.

Find two consecutive positive integers, the sum of whose squares is 365.

The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

A cottage industry produces a certain number of pottery articles in a day. The cost of production of each article is 3 rupees more than twice the number of articles produced that day. If the total cost of production is ₹90, find the number of articles produced and the cost of each article.