If x² − 5x + 4 is a factor of x⁴ − px² + q, then what are the values of p and q respectively?

x² − 5x + 4 = (x−1)(x−4). The roots x = 1 and x = 4 must satisfy x⁴ − px² + q = 0. For x=1: 1 − p + q = 0, so q = p − 1. For x = 4: 256 − 16p + q = 0. Substituting: 256 − 16p + p − 1 = 0, so 255 = 15p, p = 17. Then q = 16.