Question

If $\alpha$ , $\beta$ are the roots of quadratic equation $x^2+px+q=0$ and $\gamma$, $\delta$ are the roots of $x^2+px-r=0$ then $\left(\alpha -\gamma \right)$.$\left(\alpha -\delta \right)$ is equal to:

• A. $q+r$
• B. $q-r$
• C. $-(q+r)$
• D. $-(p+q+r)$

Answer 1

Answer: (C)

$-(q+r)$

given $x^2+px+q=(x-\alpha )(x-\beta )$ and $x^2+px-r=(x-\gamma )(x-\delta )$

put $x=\alpha$ in equation $2⟹$ we get ${\alpha }^2+\alpha x-r=(\alpha -\gamma )(\alpha -\delta )$

from equation $1⟹-(q+r)$