This is from a Real Analysis class:
For $f,g \in R[a,b],$ show that $\left|\int_a^b f g \right| \le \sqrt{\int_a^b f^2 \int_a^b g^2}$
I was given the hint to expand $\int_a^b (xf+g)^2$ to a quadratic in $x$ and use its discriminant. Obviously the discriminant $D=0$ here, but I have no idea how this helps. Can anyone enlighten me on this?