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, 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

Therefore, for, the value of the polynomial is 0 and hence, is a zero of the given polynomial.

(iv) p(x) = 3x − 2

p(x) = 0

3x − 2 = 0

Therefore, for, the value of the polynomial is 0 and hence, 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

Therefore, for, the value of the polynomial is 0 and hence, is a zero of the given polynomial.