Question

Find the value of p such that $x-2$ divides the polynomial $q\left(x\right)=x^2-px+3$.

• A. $\frac{5}{2}$
  
• B. $\frac{7}{2}$
  
• C. $\frac{1}{5}$
  
• D. $\frac{7}{5}$
  

Answer 1

The correct option is B $\frac{7}{2}$


$q\left(x\right)=x^2-px+3$
$(x-2)$ divides $q\left(x\right)$
$\Rightarrow$ $(x-2)$ is a factor of $q\left(x\right)$
By factor theorem,
$q\left(2\right)=0$
$\Rightarrow (2{)}^2-p(2)+3=0$
$\Rightarrow 4-2p+3=0\Rightarrow -2p=-7$
$2p=7$
$\therefore p=\frac{7}{2}$
So, the correct answer is option (b).