Question

If sum of the roots of of quadratic equation $\alpha x^2+2x-3\alpha =0$ is equal to their product, then the value of $\alpha$ is equal to

Answer 1

$a{x}^2+2x-3\alpha =0$

$a=a,b=2,c=-3\alpha$

Given,

$\alpha +\beta =\alpha \beta$

$-\frac{b}{a}=\frac{c}{a}$

$-b=c$

$-\left(2\right)=(-3\alpha )$

$\therefore \alpha =\frac{2}{3}$