Question

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

• A. $\pm 6$
• B. $\pm 2$
• C. $2,-6$
• D. $6,2$

Answer 1

The correct option is A $\pm 6$

Let $\alpha ,\beta$ are roots of $x^2-px+8=0$
Then $\alpha +\beta =p;\alpha \beta =8\Rightarrow (\alpha -\beta )=2\Rightarrow {(\alpha -\beta )}^2=4\Rightarrow {(\alpha +\beta )}^2-4\beta \alpha =4\Rightarrow p^2-4\times 8=4\Rightarrow p^2=4+32\Rightarrow p=\pm 6$