Question

If the remainder when $p\left(x\right)$ is divided by $x-2$ is a zero of the polynomial $q\left(x\right)=2x^2-1$, what is the value of $p\left(2\right)$, if p(2) > 0 ?

• A. $\sqrt{(}\frac{1}{4})$
• B. $\sqrt{(}\frac{1}{2})$
• C. $\frac{1}{2}$
• D. $\frac{1}{4}$

Answer 1

The correct option is B $\sqrt{(}\frac{1}{2})$

The remainder when , $p\left(x\right)$ is divided by $x-2$ is $p\left(2\right)$.

Also given, $p\left(2\right)$ is a zero of $q\left(x\right)$.
$\Rightarrow$ $q\left(p\right(2\left)\right)=0$
$\Rightarrow$ $2\left(p\right(2){)}^2-1=0$
$\Rightarrow$ $p(2{)}^2=\frac{1}{2}$
$\Rightarrow$ $p\left(2\right)=\sqrt{(}\frac{1}{2})$