Application Of Derivatives

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