Question

Check whether $-2$ and $2$ are the zeros of the polynomial $x^4-16$.

Answer 1

Let us substitute $x=-2$ in the given polynomial $f\left(x\right)=x^4-16$ as shown below:

$f(-2)=(-2{)}^4-16=16-16=0$

Since $f(-2)=0$

$\therefore$, $-2$ is the zero of the polynomial $f\left(x\right)=x^4-16$.

Now substitute $x=2$ as shown follows:

$f\left(2\right)=(2{)}^4-16=16-16=0$

Since $f\left(2\right)=0$,

$\therefore$, $2$ is the zero of the polynomial $f\left(x\right)=x^4-16$.

Hence, $-2$ and $2$ are the zeroes of the polynomial $f\left(x\right)=x^4-16$.