Roots of Polynomial for a Derivative

An elliptic curve can be written as y^2=x^3+ax+b. I need a proof for why x^3+ax+b either have 3 real roots or 1 real root and 2 complex roots. I don't have anything that I know about it prior to asking for help here at SolutionLibrary.

© SolutionLibrary Inc. 9836dcf9d7