KöMaL 2011 C1073

The function $f$ ( $x$ )= $x^3$ + $ax^2$ + $bx$ + $c$ ( $a, b, c \in \mathbb{R}$ ) has at least two zeros. Prove that $a^2$ >3 $b$ .

Official text KöMaL. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.