JEE Main 20208 Jan, Evening shiftMathematicsMediumComplex Numbers and Quadratic Equations264× since 2002Let 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 :AOption A. x² + 101x + 100 = 0BOption B. x² + 102x + 101 = 0COption C. x² – 102x + 101 = 0DOption D. x² – 101x + 100 = 0CheckSkip · show solution
