Question

Verify whether the following value is the zero of the polynomial, indicated against them:

$p\left(x\right)=2x+1$, $x=\frac{1}{2}$.

Answer 1

Verifying $x=\frac{1}{2}$ is the zero of $p\left(x\right)=2x+1$or not:

In general, we can say that a zero of a polynomial $p\left(x\right)$ is a number $c$, such that $p\left(c\right)=0$.

Therefore, if $x=\frac{1}{2}$ is the zero of $p\left(x\right)=2x+1$, then $p\left(\frac{1}{2}\right)=0$

$\begin{array}{rcl}p\left(x\right)& =& 2x+1\\ p\left(\frac{1}{2}\right)& =& 2\times \frac{1}{2}+1\\ & =& 1+1\\ & =& 2\ne 0\end{array}$

Therefore, $x=\frac{1}{2}$ is not the zero of $p\left(x\right)=2x+1$.