Question:

If $\displaystyle ax^3 + bx^2 + d=0$ has a double root, show that $\displaystyle 27a^2d+4b^3 = 0$

I do not know how to start this question. However, I know that it uses this theorem:

If a polynomial has a root $\displaystyle \alpha $ of multiplicity m, then P'(x) has the root $\displaystyle \alpha $ with multiplicity (m-1).

Any help is appreciated.