## Prove it

For students of class 11-12 (age 16+)
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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 $\left | b^{2}-4ac \right |\leq \left | B^{2}-4AC \right |$
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