JEE Advanced 2024 Mathematics question on Probability

Let $X$ be a random variable, and let $P(X=x)$ denote the probability that $X$ takes the value $x$. Suppose that the points $(x, P(X=x))$, $x = 0,1,2,3,4$, lie on a fixed straight line in the $xy$-plane, and $P(X=x) = 0$ for all $x \in \mathbb{R} - \{0,1,2,3,4\}$. If the mean of $X$ is $\frac{5}{2}$, and the variance of $X$ is $\alpha$, then the value of $24\alpha$ is _______.