Prove it
Posted: Mon Jun 04, 2012 2:50 pm
Let $a,b,c,A,B,C\in \mathbb{R},a\neq 0,A\neq 0.$ For every real number $x$,$\left | ax^{2}+bx+c \right |\leq \left | Ax^{2}+Bx+C \right |$. Prove that \[\left | b^{2}-4ac \right |\leq \left | B^{2}-4AC \right |\]