Solution of Chapter 2. Polynomials (NCERT - Mathematics Book)

The graphs of y = p(x) are given in Fig. 2.10 below, for some polynomials, p(x). Find the number of zeroes of p(x) in each case.

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

(i) x² - 2x - 8

(ii) 4s² - 4s + 1

(iii) 6x² - 3 - 7x

(iv) 4u² + 8u

(v) t² - 15

(vi) 3x² - x - 4

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

Divide the polynomial by the polynomial and find the quotient and remainder in each of the following :

(i)

(ii)

(iii)

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:

(i)

(ii)

(iii)

Obtain all other zeroes of if two of its zeroes areand

On dividing by a polynomial the quotient and remainder were and respectively. Find

Give examples of polynomials and which satisfy the division algorithm and

(i)

(ii)

(iii)

Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case:

(i)

(ii)

Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, -7, -14 respectively.

If the zeroes of the polynomial are find and

If two zeroes of the polynomial are find other zeroes.

If the polynomial is divided by another polynomial the remainder comes out to be find and