Question

Find the zeros of the polynomial in each of the following:
(i) $p\left(x\right)=2x-3$
(ii) $q\left(x\right)=5-9x$
(iii) $g\left(y\right)=3y$
(iv) $f\left(t\right)=t^2-2t$
(v) $r\left(x\right)={\left(x-2\right)}^2+{\left(x+2\right)}^2$
(vi) $h\left(x\right)=cx+d,c\ne 0,c,d$are real numbers.

Answer 1

$i).p\left(x\right)=2x-3$

$\Rightarrow$ zeroes $=2x-3=0$

$\Rightarrow x=\frac{-3}{2}$

$ii).q\left(x\right)=5-9x$

$\Rightarrow$ zeroes $=5-9x=0$

$\Rightarrow x=\frac{5}{9}$

$iii).g\left(y\right)=3y$

$\Rightarrow$ zeroes $=3y=0$

$\Rightarrow y=0$

$iv).f\left(t\right)=t^2-2t$

$\Rightarrow$ zeroes $=t(t-2)=0$

$\Rightarrow t=0,2$

$v).r\left(x\right)={(x-2)}^2+{(x+2)}^2$

$\Rightarrow$ zeroes $=x^2+4-4x+x^2+4+4x=0$

$\Rightarrow 2x^2+8=0$

$\Rightarrow x^2+4=0$

$\Rightarrow x=2i,-2i$

$vi).h\left(x\right)=cx+d$

$\Rightarrow$zeroes $=cx+d=0$

$\Rightarrow x=\frac{-d}{c}$

Hence, solved.