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
Just remember you have to start this particular problem by adding to both sides so that your equation is in the proper form.
John
My calculator said it, I believe it, that settles it
