Question

The sum of the squares of the roots of the equation $x^2-5x+p=0$ is $13$. Then what is the value of $p$?

• A. $4$
• B. $-4$
• C. $6$
• D. $-6$

Answer 1

The correct option is C $6$

Given $x^2-5x+p=0$ and $a^2+b^2=13$ if $a$ and $b$ are its roots.
$\Rightarrow a+b=5,ab=p$

Using the identity $(a+b{)}^2=a^2+b^2+2ab$
$\Rightarrow (5{)}^2=13+2p$
$25=13+2p$
$\Rightarrow p=6$