Question

Verify whether the following are zeroes of the polynomial, indicated against them:
$p\left(x\right)=2x+1,x=\frac{1}{2}$.

Answer 1

Given, $p\left(x\right)=2x+1$.

We know, $a$ is a root of $f\left(x\right)$, only if $f\left(a\right)=0$.

Here,

$p\left(x\right)=0$

$⟹$ $2x+1=0$

$⟹$$2x=-1$

$⟹$$x=\frac{-1}{2}$, that is,$x=\frac{1}{2}$ is not the zero of the given polynomial.

To verify this, we find $p\left(\frac{1}{2}\right)$.

If $p\left(\frac{1}{2}\right)=0$, then $x=\frac{1}{2}$ is a zero of the given polynomial.

That is, $p\left(\frac{1}{2}\right)$ $=2\left(\frac{1}{2}\right)+1=1+1=2\ne 0$.

Hence, proved that the given $x$ is not a zero of the given polynomial.