Question

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

Answer 1

We have,

$\mathrm{p}\left(\mathrm{x}\right)={\mathrm{x}}^2-1,\mathrm{x}=1,-1$

Putting the value $\mathrm{x}=1$ in the polynomial $\mathrm{p}\left(\mathrm{x}\right)={\mathrm{x}}^2-1$, we get

$$\begin{gathered} \mathrm{p}\left(1\right)=1^2-1 \\ \Rightarrow \mathrm{p}\left(1\right)=1-1 \\ \Rightarrow \mathrm{p}\left(1\right)=0 \end{gathered}$$

Hence, $\mathrm{x}=1$ is a zero of the polynomial $\mathrm{p}\left(\mathrm{x}\right)={\mathrm{x}}^2-1$.

Now,

Putting the value $\mathrm{x}=-1$ in the polynomial $\mathrm{p}\left(\mathrm{x}\right)={\mathrm{x}}^2-1$, we get

$$\begin{gathered} \mathrm{p}(-1)={(-1)}^2-1 \\ \Rightarrow \mathrm{p}(-1)=1-1 \\ \Rightarrow \mathrm{p}(-1)=0 \end{gathered}$$

Hence, $\mathrm{x}=-1$ is a zero of the polynomial $\mathrm{p}\left(\mathrm{x}\right)={\mathrm{x}}^2-1$.