International Mathematical Olympiad 1959 Problem 3

Let $a,b,c$ be real numbers. Consider the quadratic equation in $\cos x$:

$$a\cos^{2}x+b\cos x+c=0.$$

Using the numbers $a,b,c,$ form a quadratic equation in $\cos 2x$, whose roots are the same as those of the original equation. Compare the equations in $\cos x$ and $\cos 2x$ for $a=4,b=2,c=-1$.