
Hi,
Every polynomial equation has a discriminant D, which is the product squared of the diferences of all pairs of roots. ( If the roots are labeled x_{1}, x_{2}, ... up to x_{n}, then D = P^{2} where P = the product of x_{i}  x_{j} for i < j.) The easiest way to compute D for a cubic is to reduce the cubic to the form y^{3} + py = q. (To do this, divide through by the coefficient of x^{3} to get x^{3} + ax^{2} + bx + c = 0, then make the substitution x = y  (a/3).) The discriminant is D = 4p^{3}  27 q^{2}. The original polynomial has three real roots if D is greater or equal zero, and two imaginary roots if D is negative. (A cubic always has at lest one real root.) When D = 0 there are repeated roots.
Chris

