Question

Question 4
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 $\ne$ 0
(vii) p(x) = cx + d, c $\ne$ 0, c, d are real numbers.

Answer 1

(i) x + 5 = 0, x = - 5, so, - 5 is the zero of x + 5.

(ii) x - 5 = 0, x = - 5 so, 5 is the zero of x - 5.

(iii) $2x+5=0,\Rightarrow 2x=-5,\Rightarrow x=\frac{-5}{2},so-\frac{5}{2}$ is the zero of 2x + 5.

(iv) $3x-2=0\Rightarrow 3x=2\Rightarrow x=\frac{2}{3},so\frac{2}{3}$ is the zero of 3x - 2.

(v) $3x=0,\Rightarrow x=0,$ so 0 is the zero of 3x.

(vi) $ax=0(a\ne 0)\Rightarrow x=\frac{0}{a}=0,$ so, is the zero of ax.

(vii) $cx+d=0(c\ne 0)\Rightarrow cx=-d\Rightarrow x=\frac{-d}{c},so,\frac{-d}{c}$ is the 0 of cx + d.