I want to find the number of quadratic equations which are unchanged by cubing their roots.
Let $ax^2 + bx + c $ be a quadratic whose roots are $ \alpha$ and $\beta $.
I know that quadratic whose roots are $\alpha^3$ and $\beta^3 $ is $a^3x^2 + (b^3 - 3abc)x + c^3 = 0$.
On comparing coefficients I am facing difficulties.
Pls help me !!