TIMO 2019 - Senior Secondary (Grades 10-12) - Heat Round - Paper 3 Question 6

$\alpha,\beta$ are nonzero roots of $x^2-20x-30=0$. The numbers $\frac{\alpha+\beta}{\alpha^2\beta}$ and $\frac{\alpha+\beta}{\alpha\beta^2}$ are roots of $x^2-Sx+T=0$. Find $S+T$.