If $f(x)=ax^2+bx+c$ has an irrational root, if $u=\frac{p}{q}$ be any rational number. a,b,c,p and q are integers. Prove that $\frac{1}{q^2}\le|f(u)|$
My approach $b^2-4ac>0$,$b^2-4ac\ne k^2$, $k$ is a rational number.
$f(u)=a(\frac{p}{q})^2+b(\frac{p}{q})+c$, could not approach after this step.