If the function f(x)=2 x^3-9 a x^2+12 a^2 x+1, a>0 has a local maximum at x=α and a local minimum at x=α^2, then α and α^2 are the roots of the…

If the function $\displaystyle f(x)=2 x^3-9 a x^2+12 a^2 x+1, a>0$ has a local maximum at $\displaystyle x=\alpha$ and a local minimum at $\displaystyle x=\alpha^2$, then $\displaystyle \alpha$ and $\displaystyle \alpha^2$ are the roots of the equation :