Let , where . If for all , find the maximum value of…

MATHEMATICS · Subjective · AoPS · Mathematics · More Inequalities · More Inequalities

Problem

Let

f(x)=x^4+ax^3+3x^2+bx+1

, where

a,b\in\mathbb{R}

. If

f(x)\geq0

for all

x\in\mathbb{R}

, find the maximum value of

a^2+b^2