Question

The quadratic equation whose roots are ${\alpha }^2+\alpha \beta$ & ${\beta }^2+\alpha \beta is:$

Answer 1

Consider the given roots.

${\alpha }^2+\alpha \beta$ and ${\beta }^2+\alpha \beta$

We know that

$x^2-\left(sumofroots\right)x+productofroots=0$

$x^2-({\alpha }^2+\alpha \beta +{\beta }^2+\alpha \beta )x+({\alpha }^2+\alpha \beta )({\beta }^2+\alpha \beta )=0$

$x^2-({\alpha }^2+{\beta }^2+2\alpha \beta )x+({\alpha }^2+\alpha \beta )({\beta }^2+\alpha \beta )=0$

Hence, this is the answer.