Question

Verify whether the values of $x$ given in each case are the zeroes of the polynomial or not?
$f\left(x\right)=2x-1,x=\frac{1}{2},\frac{-1}{2}$

Answer 1

Given polynomial $2x-1$ and value $x=\frac{1}{2},-\frac{1}{2}$

$p\left(x\right)=2x-1$

Replace x by $\frac{1}{2}$ we get

$p\left(\frac{1}{2}\right)=2\times \frac{1}{2}-1$

$\Rightarrow p\left(\frac{1}{2}\right)=1-1=0$

$p\left(x\right)=2x-1$

Replace x by $-\frac{1}{2}$

$p(-\frac{1}{2})=2\times -\frac{1}{2}-1$

$\Rightarrow p(-\frac{1}{2})=-1-1=-2$

Then polynomial $p\left(x\right)=2x-1$ value zero for value $x=\frac{1}{2}$ and non zero value for $x=-\frac{1}{2}$

So polynomial $p\left(x\right)=2x-1$ value zero polynomial for value $x=\frac{1}{2}$ and not zero polynomial value for $x=-\frac{1}{2}$