Question

If the sum of the squares of the roots of $x^2+px-3=0$ is $10$, then the value of $p$ is equal to

• A. $\pm 2$
• B. $\pm 4$
• C. $\pm 1$
• D. $\pm 3$

Answer 1

The correct option is A $\pm 2$

Let the roots of the given equation be $a$ and $b$.
Then,
Given $a^2+b^2=10......\left(1\right)$
Sum of the roots $\Rightarrow a+b=-p......\left(2\right)$
Product of the roots $\Rightarrow ab=-3......\left(3\right)$
We know that,
$a^2+b^2=(a+b{)}^2-2ab$
$\Rightarrow 10=(-p{)}^2-2(-3)$
[Using (1), (2) and (3)]
$\Rightarrow 10=p^2+6$
$\Rightarrow p^2=4$
$\Rightarrow p=\pm 2$