Question

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

Answer 1

We have, $\mathrm{p}\left(\mathrm{x}\right)=\mathrm{lx}+\mathrm{m},\mathrm{x}=\frac{-\mathrm{m}}{\mathrm{l}}$

If the given value of $\mathrm{x}$ is the zero of the given polynomial, then on substituting the value of $\mathrm{x}$ in the given polynomial then value of polynomial becomes zero.

So, put the value of $x=\frac{-\mathrm{m}}{\mathrm{l}}$ in $\mathrm{p}\left(\mathrm{x}\right)=\mathrm{lx}+\mathrm{m}$

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

Hence, $x=\frac{-\mathrm{m}}{\mathrm{l}}$ is a zero of the polynomial $\mathrm{p}\left(\mathrm{x}\right)=\mathrm{lx}+\mathrm{m}$.