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

Let $\displaystyle \alpha=\frac{-1+i \sqrt{3}}{2}$. If $\displaystyle \mathrm{a}=(1+\alpha) \sum_{\mathrm{k}=0}^{100} \alpha^{2 \mathrm{k}}$ and $\displaystyle \mathrm{b}=\sum_{\mathrm{k}=0}^{100} \alpha^{3 \mathrm{k}}$, then a and b are the roots of the quadratic equation :