R has degree 4 and zeros 1 − 5i and 1, with 1 a zero of multiplicity 2, find a polynomial

Answer 1

In order to have a zero of -5i, you also need one of 5i.

(x - 1)(x - 1)(x + 5i)(x - 5i) = (x² -- 2x + 1)(x² + 25i²) = x⁴ - 25x² - 2x³ + 50x + x² - 25 = x⁴ - 2x³ + 24x² + 50x - 25