Question

Verify whether the following are zeroes of the polynomial, indicated against them.
$p\left(x\right)=lx+m,x=-\frac{m}{l}$

Answer 1

Given, $p\left(x\right)=lx+m$.

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

Here,

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

$⟹$ $lx+m=0$

$⟹$$lx=-m$

$⟹$$x=\frac{-m}{l}$, that is,$x=-\frac{m}{l}$ is the zero of the given polynomial.

To verify this, we find $p(-\frac{m}{l})$.

If $p(-\frac{m}{l})=0$, then$x=-\frac{m}{l}$ is a zero of the given polynomial.

That is, $p(-\frac{m}{l})$$=l(-\frac{m}{l})+m=-m+m=0$.

Hence, proved that the given $x$ is a zero of the given polynomial.