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 \( \dfrac{5}{2} \), and the variance of \( X \) is \( \alpha \), then the value of \( 24\alpha \) ___________.
