If $\alpha, \beta$ are roots of the equation $x^2 + px - q = 0$. $\gamma , \delta$ are roots of equation $x^2 + px -r$, then find the value of $(\alpha - \gamma )(\alpha - \delta)$.
Answer - $q-r$
My try -
$\alpha + \beta= -p$ and $\alpha \beta = -q$
$\gamma + \delta = -p$ and $\gamma \delta = -r$
Then to we've to find:
$(\alpha - \gamma)(\alpha - \delta) = \alpha^2 - \alpha \delta - \alpha \gamma + \gamma \delta $ out of which only $\gamma \delta$ is known, then how to find the rest?
Also, when noticed carefully about the question, we find that question is $(\alpha - \gamma)(\alpha - \delta)$ which doesn't have $\beta$ in its product, which makes the question more confusing.
Thanks in Advance :)