1. The problem statement, all variables and given/known data Show that cos(π/5) = λ/2, where λ = (1 +√5)/2 (the Golden Ratio). 2. Relevant equations [Hint: As cos 5θ = 1, where θ = 2π/5, we see from De Moivre’s theorem that P(cos θ) = 0 for some polynomial P of degree five. Now observe that P(z) = (1 − z)Q(z)2 for some quadratic polynomial Q.] 3. The attempt at a solution Not sure how!! from P(cos θ) = 0 there are 5 solutions for p(z) and one solution for θ. but then only one of the 6 multiplying factors needs to be zero right? i.e. ## (z - a)(z - b)(z - c)(z - d)(z - e)(Cos θ) = 0 ## only one of them needs to be zero because anything multiplied zero is also zero.