Question

Verify whether the following are zeroes of the polynomial, indicated against them: $\mathrm{p}\left(\mathrm{x}\right)=3\mathrm{x}+1,\mathrm{x}=\frac{-1}{3}$

Answer 1

We have,

$\mathrm{p}\left(\mathrm{x}\right)=3\mathrm{x}+1,\mathrm{x}=\frac{-1}{3}$

For $\mathrm{x}=\frac{-1}{3},$ the given polynomial $\mathrm{p}\left(\mathrm{x}\right)=3\mathrm{x}+1$ will be

$$\begin{gathered} \mathrm{p}\left(\frac{-1}{3}\right)=3\left(\frac{-1}{3}\right)+1 \\ \Rightarrow \mathrm{p}\left(\frac{-1}{3}\right)=-1+1 \\ \Rightarrow \mathrm{p}\left(\frac{-1}{3}\right)=0 \end{gathered}$$

Since, $\mathrm{p}\left(\mathrm{x}\right)=3\mathrm{x}+1$is $0$ at $\mathrm{x}=\frac{-1}{3}$

Hence, $\frac{-1}{3}$is a zero of $p\left(\mathrm{x}\right).$