Question

Let α = (- 1 + i√3)/2. If a = (1 + α) ∑α^2k for k∈[k=0, 100] and b = ∑α^3k for k∈[k=1, 100], then a and b are the roots of the quadratic equation :

(1) x² – 102x + 101 = 0

(2) x² + 101x + 100 = 0

(3) x² – 101x + 100 = 0

(4) x² + 102x + 101 = 0

Answer 1

Answer is (1) x² - 102x + 101 = 0

Answer 2

Answer is (1) x² – 102x + 101 = 0