JEE Math Practice Question

Let $$\alpha = {{ - 1 + i\sqrt 3 } \over 2}$$. If $$a = \left( {1 + \alpha } \right)\sum\limits_{k = 0}^{100} {{\alpha ^{2k}}} $$ and $$b = \sum\limits_{k = 0}^{100} {{\alpha ^{3k}}} $$, then a and b are the roots of the quadratic equation :

1. A.x2 + 101x + 100 = 0
2. B.x2 + 102x + 101 = 0
3. C.x2 – 102x + 101 = 0
4. D.x2 – 101x + 100 = 0