Question

If difference of roots of the equation $x^2+px+8=0$ is $2$, then $p$ is equal to

• A. $\pm 2$
• B. $\pm 4$
• C. $\pm 6$
• D. $\pm 8$

Answer 1

Answer: (C)

$\pm 6$

Let roots be $\alpha ,\beta$
$\alpha -\beta =2$
$(\alpha -\beta {)}^2=(\alpha +\beta {)}^2-4\alpha \beta$
$\alpha +\beta =-p,\alpha \beta =8$
$\Rightarrow 2^2=(-p{)}^2-4\times 8$
$\Rightarrow p=\pm 6$