It doesn't have to be.
It's possible that the quadratic is always negative for all real $x$.
But what is true is that if the quadratic has only complex roots (has not real roots) then it must be either positive for all real $x$ or negative for all real $x$.
Well, if it were positive for some real $x_1$ and it were negative for some real $x_2$, then it'd have to be zero for some real $c$ in between $x_1$ and $x_2$. That that would mean $c$ is a real root.
(Furthermore, you can tell if it will always be positive or negative by checking if coeeficient of $x^2$ ... or the constant term.)