Question

Find the zero of the polynomial in each of the following cases: 

(i) p(x) = x + 5 (ii) p(x) = x – 5 (iii) p(x) = 2x + 5 (iv) p(x) = 3x – 2 (v) p(x) = 3x

(vi) p(x) = ax, a ≠ 0 (vii) p(x) = cx + d, c ≠ 0, c, d are real numbers.

Answer 1

Zero of a polynomial is that value of the variable at which the value of the polynomial is obtained as 0. 

(i) p(x) = x + 5 p(x) = 0 x + 5 = 0 x = − 5 Therefore, for x = −5, the value of the polynomial is 0 and hence, x = −5 is a zero of the given polynomial.

(ii) p(x) = x − 5 p(x) = 0 x − 5 = 0 x = 5 Therefore, for x = 5, the value of the polynomial is0 and hence, x = 5 is a zero of the given polynomial.

(iii) p(x) = 2x + 5 p(x) = 0 2x + 5 = 0 2x = − 5 = x = -\(\frac{5}{2}\). Therefore, for x = -\(\frac{5}{2}\), the value of the polynomial is 0 and hence, x = -\(\frac{5}{2}\) is a zero of the given polynomial.

(iv) p(x) = 3x − 2 p(x) = 0 = 3x − 2 = 0 = x = \(\frac{2}{3}\) .Therefore, for x = \(\frac{2}{3}\), the value of the polynomial is 0 and hence, x = \(\frac{2}{3}\) is a zero of the given polynomial.

(v) p(x) = 3x p(x) = 0 3x = 0 x = 0 Therefore, for x = 0, the value of the polynomial is 0 and hence, x = 0 is a zero of the given polynomial.

(vi) p(x) = ax p(x) = 0 ax = 0 x = 0 Therefore, for x = 0, the value of the polynomial is 0 and hence, x = 0 is a zero of the given polynomial.

(vii) p(x) = cx + d p(x) = 0 cx+ d = 0 = x = -\(\frac{d}{c}\). Therefore, for x = -\(\frac{d}{c}\) , the value of the polynomial is 0 and hence, x = -\(\frac{d}{c}\) is a zero of the given polynomial.