MathematicsMedium129×since 2002Q5146Let α=−1+i32\alpha = {{ - 1 + i\sqrt 3 } \over 2}α=2−1+i3. If a=(1+α)∑k=0100α2ka = \left( {1 + \alpha } \right)\sum\limits_{k = 0}^{100} {{\alpha ^{2k}}}a=(1+α)k=0∑100α2k and b=∑k=0100α3kb = \sum\limits_{k = 0}^{100} {{\alpha ^{3k}}}b=k=0∑100α3k, then a and b are the roots of the quadratic equation :Ax² + 101x + 100 = 0Bx² + 102x + 101 = 0Cx² – 102x + 101 = 0Dx² – 101x + 100 = 0Check answerSkip