Question

Find the zero of the polynomial in each of the following cases:
(i) $p\left(x\right)=x+5$
(ii) $p\left(x\right)=x-5$
(iii) $p\left(x\right)=2x+5$
(iv) $p\left(x\right)=3x-2$
(v) $p\left(x\right)=3x$
(vi) $p\left(x\right)=ax,a\ne 0$
(vii) $p\left(x\right)=cx+d,c\ne 0,c,d$ are real numbers.

Answer 1

To find zero of the polynomial, $p\left(x\right)=0$

$\left(i\right)$ If $p\left(x\right)=x+5=0$ then $x=-5$, i.e. $-5$ is the zero.

$\left(ii\right)$ If $p\left(x\right)=x-5=0$ then $x=5$, i.e. $5$ is the zero.

$\left(iii\right)$ If $p\left(x\right)=2x+5=0$ then $x=\frac{-5}{2}$, i.e. $\frac{-5}{2}$ is the zero.

$\left(iv\right)$If $p\left(x\right)=3x-2=0$ then $x=\frac{2}{3}$, i.e. $\frac{2}{3}$ is the zero.

$\left(v\right)$ If $p\left(x\right)=3x=0$ then $x=0$, i.e. $0$ is the zero.

$\left(vi\right)$ If $p\left(x\right)=ax=0$ then $x=0$, i.e. $0$ is the zero.

$\left(vii\right)$If $p\left(x\right)=cx+d=0$ then $x=\frac{-d}{c}$, i.e. $\frac{-d}{c}$ is the zero.