Find the zero of the polynomial:

Question:

Find the zero of the polynomial:

(i) $p(x)=x-5$

(ii) $q(x)=x+4$

(iii) $r(x)=2 x+5$

(iv) $f(x)=3 x+1$

(v) $g(x)=5-4 x$

(vi) $h(x)=6 x-2$

(vii) $p(x)=a x, a \neq 0$

(viii) $q(x)=4 x$

Solution:

(i) $p(x)=0 \Rightarrow x-5=0$

$\Rightarrow x=5$

Hence, 5 is the zero of the polynomial $p(x)$.

(ii) $q(x)=0 \Rightarrow x+4=0$

$\Rightarrow x=-4$

Hence, $-4$ is the zero of the polynomial $q(x)$.

(iii) $r(x)=0 \Rightarrow 2 x+5=0$

$\Rightarrow t=\frac{-5}{2}$

Hence, $\frac{-5}{2}$ is the zero of the polynomial $p(t)$.

(iv) $f(x)=0 \Rightarrow 3 x+1=0$

$\Rightarrow x=-\frac{1}{3}$

Hence, $-\frac{1}{3}$ is the zero of the polynomial $f(x)$.

(v) $g(x)=0 \Rightarrow 5-4 x=0$

$\Rightarrow x=\frac{5}{4}$

Hence, $\frac{5}{4}$ is the zero of the polynomial $g(x)$.

(vi) $h(x)=0 \Rightarrow 6 x-2=0$

$\Rightarrow x=\frac{2}{6}=\frac{1}{3}$

Hence, $\frac{1}{3}$ is the zero of the polynomial $h(x)$.

(vii) $p(x)=0 \Rightarrow a x=0$

$\Rightarrow x=0$

Hence, 0 is the zero of the polynomial $p(x)$.

(viii) $q(x)=0 \Rightarrow 4 x=0$

$\Rightarrow x=0$

Hence, 0 is the zero of the polynomial $q(x)$.