discriminants

Hey guys, I have a pretty elementary question:
Why is it that if a quadratic polynomial is never negative, then its discriminant cannot be positive?  My book states it as though it's obvious, and it probably is but I'm just not seeing it.

*polynomial of a single variable, in case that wasn't clear

P(x) = (x - x1)(x - x2). P(x) < 0 for x in (x1, x2).

>>3
I have no idea what you're trying to get across to me.

If the discriminant is positive then the quadratic has two distinct real roots, and switches sign on the interval between the roots.

>>1

Try to make a U cross a line twice, while resting on one half-plane of the line.