Grignard reagents react with aldehydes to form secondary alcohols, while ketones form tertiary alcohols.
The final product of the sequence is 2-butanol (\( CH_3−CH_2−CH(OH)−CH_3 \)).
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: