A2B → 2A+ + B2−, B2− has a complete octet in its di-anionic form, thus in its atomic state it has 6 electrons in its valence shell. As it has a negative charge, it has acquired two electrons to complete its octet.
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: