Latent heat is the energy absorbed or released during a phase change per unit mass. Hence, it is specific energy:
\[ \text{Latent Heat} = \frac{\text{Energy}}{\text{Mass}}. \]
The dimensional formula of energy is:
\[ \text{Energy} = [ML^2T^{-2}]. \]
Divide by mass:
\[ \text{Latent Heat} = \frac{[ML^2T^{-2}]}{[M]} = [M^0L^2T^{-2}]. \]
Final Answer: \([M^0L^2T^{-2}]\).
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: