the function $f(x)=x^2+2a\cos x-2bx$ with multiple critical points

Question

Suppose that $f(x)=x^2+2a\cos x-2bx$, where $a,b$ constants.Prove that if $|a|>1$, the function has multiple critical points.

Answer 1

This does not seem correct. $f'(x)=2x-2a\sin x-2b=0$ could have just one root. graphing $ y=x-1.1\sin x -2$ gives one root.