In the first step, the reaction of bromobenzene (\( C_6H_5Br \)) with methyl bromide (\( CH_3Br \)) in the presence of alcoholic NaOH undergoes a nucleophilic substitution to form B, which is ortho-bromophenol.
In the second step, treating ortho-bromophenol with \( \text{HBr} \) in ether leads to the formation of C, which is para-bromophenol.
Compound A (bromobenzene) and compound C (para-bromophenol) are position isomers because they differ in the position of the bromine and hydroxyl groups on the benzene ring.
The structures of B and C are as shown in Option (3), and A and C are position isomers.
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: