Question

The sum of the squares of the roots of the equation $x^2-px+5=0$ is $6$. Then what is the value of $p$? $(p>0)$

• A. $4$
• B. $3$
• C. $6$
• D. $2$

Answer 1

The correct option is A $4$

Given $x^2-px+5=0$ and $a^2+b^2=6$ if $a$ and $b$ are its roots.
$\Rightarrow a+b=p,ab=5$

Using the identity $(a+b{)}^2=a^2+b^2+2ab$
$\Rightarrow (p{)}^2=6+2.5=6+10$
$p^2=16$
$\Rightarrow p=4$