# NCERT Solutions for Class 10th Mathematics

## Chapter 2. Polynomials

### Exercise 2.2

**Chapter 2. Polynomials**

**Exercise 2.2**

Q1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

(i) *x*^{2} – 2*x *– 8

**Solution:**

Using Middle term splitting method:

x^{2} – 4x + 2x – 8 = 0

⇒ x(x – 4) + 2(x – 4) = 0

⇒ x(x – 4) + 2(x – 4) = 0

⇒ (x – 4) (x + 2) = 0

⇒ x – 4 = 0 x + 2 = 0

⇒ x = 4, x = – 2

Zeroes; α = 4 β = – 2

Verifying the relationship between the zeroes and the coefficients.

a = 1, b = – 2, and c = – 8

(ii) 4*s*^{2} – 4*s *+ 1

(iii) 6*x*^{2} – 3 – 7*x*

(iv) 4*u*^{2} + 8*u *

(v) *t*^{2 }– 15

(vi) 3*x*^{2} – *x *– 4

Q2. **. **Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.