Question

If the sum of the roots of the equation $x^2+px+q=0$ is equal to the sum of their squares, then

Answer 1

$x^2+px+q=0$ ...(1)

Let $\alpha ,\beta$ be roots of equation (1)

then acc to question

$\alpha +\beta ={\alpha }^2+{\beta }^2$ .....(2)

Now term eq. (1) $\alpha +\beta =-p$

$\alpha \beta =q$

From eq (2)

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

$-p=(-p{)}^2-2q$

$-p=p^2-2q$

$p^2+p-2q=0$