# NCERT Solutions class 10 Maths Ch- 2 Polynomials

## Ex 2.1

### Question 1: The graphs of y = p(x) are given below for some polynomials p(x). Find the number of zeroes of p(x) in each case. Solution: ## t2 – ( )2                   . : X =  15

From Identitity    A2 - B 2 =  ( A + B ) (A - B)

## (t + ) (t - )

### Question 2. Find a quadratic polynomial each with the given numbers as the sum and product of zeroes respectively:  ## Ex 2.3

### Question 1. Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following: (i) p(x) = x3 – 3x2 + 5x – 3, g(x) = x2 – 2 (ii) p(x) = x4 – 3x2 + 4x + 5, g(x) = x2 + 1 – x (iii) p(x) = x4– 5x + 6, g(x) = 2 – x2 Solution: ### Question 2. Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial. (i) t2 – 3, 2t4 + 3t3 – 2t2– 9t – 12 (ii) x2 + 3x + 1, 3x4 + 5x3 – 7x2 + 2x + 2 (iii) x2 + 3x + 1, x5 – 4x3 + x2 + 3x + 1 Solution: ### Question 3. Obtain all other zeroes of 3x4 + 6x3 – 2x2 – 10x – 5, if two of its zeroes are  ### Question 5. Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and: (i) deg p(x) = deg q(x) (ii) deg q(x) = deg r(x) (iii) deg r(x) = 0 Solution:  