Phenol is a highly activated compound and can undergo bromination directly with bromine without any Lewis acid. However, the Lewis acid catalyst indeed polarises the bromine to generate Br+, making Statement II true.
Thus the correct answer is Option 4.
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: