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 ∈ ℝ − {0, 1, 2, 3, 4}. If the mean of X is 5/2, and the variance of X is α, then the value of 24α is ________.