It is known that:
A positive discriminant indicates that the quadratic has two distinct real number solutions. A discriminant of zero indicates that the quadratic has a repeated real number solution. A negative discriminant indicates that neither of the solutions are real numbers.
but why is that? it looks obvious in the formula because of the +- sign, and by definition of the sqrt.
I'm looking for a formal proof for that. Can someone refer me to where I can read about that?