For any quadratic polynomial equation of the form:
Find the Discriminant, and evaluate the nature of the roots as follows:
Two real and unequal roots. If is a perfect square, the quadratic factors over .
Two real and equal roots. Alternatively, one real root with a multiplicity of two. That is to say that the trinomial is a perfect square and has two identical factors.
A conjugate pair of complex roots of the form where is the imaginary number defined by
