I've been given the following problem and I can't seem to figure out the solution, would appreciate any help and direction to solution !

Let's look at the equation :y^{3}+ py + q = 0 (*)

We shall define Delta (ordin short)d = 4p^{3}+ 27q^{2}^{Prove that : a) If d > 0 , then (*) has a single solution . b) If d = 0 , and at least one of the coefficients (p , q) =/= 0, then (*) has 2 solutions . c) If d < 0 , then (*) has 3 solutions .}^{ Thank you very much in advance ! }