JEE Math Practice Question

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 :

1. A.$$x^2-6 x+8=0$$
2. B.$$8 x^2-6 x+1=0$$
3. C.$$8 x^2+6 x-1=0$$
4. D.$$x^2+6 x+8=0$$