Question

For p, q ∈ R, consider the real valued function f(x) = (x - p)² -q, x ∈ R and q > 0. Let a₁ , a₂ ,  a₃ , and a₄ be in an arithmetic progression with mean p and positive common difference. If |f(a₁)| = 500 for all i = 1, 2, 3, 4, then the absolute difference between the roots of f(x) = 0 is___.

Answer 1

Correct answer is 50