Hi!I am currently training for the mathematical olympiad,and I am stuck at the question below. Please help by writing a solution for me,using simple to understand terms.Thanks!
Let \(a, b, c\) be real numbers. Given the equation for \(\cos x\): \[a \cos^2(x )+ b \cos (x) + c = 0\] Form a quadratic equation in \(\cos (2x)\) whose roots are the same values of \(x\). Compare the equations in \(\cos x\) and \(\cos (2x)\) for \(a=4, b=2, c=-1\).