Find the Discriminant, and evaluate the nature of the roots as follows:
No calculation quick look: If the signs on and are opposite, then guaranteed.
Two real and unequal roots. If is a perfect square, the quadratic factors over (the rationals).
One real root with a multiplicity of two. That is to say that the trinomial is a perfect square and has two identical factors. Presuming rational coefficients, the root will be rational as well.
A conjugate pair of complex roots of the form where is the imaginary number defined by
John
My calculator said it, I believe it, that settles it
