Explanation:
Since f(x) has real coefficients, all complex roots of f(x) must come in complex conjugate pairs. Thus, as 5 - 2i is a root, 5 + 2i must also be a root.
Hence, f(x) = [x - (5 - 2i)][x - (5 + 2i)](x - 2)²
= (x² - 10x + 29)(x² - 4x + 4)
= x⁴ - 14x³ + 73x² - 156x + 116 (if we set a to be 1).