Find a degree 3 polynomial with real coefficients having zeros 2 and 4 - 2i and a lead coefficient of 1. Write P in expanded form.

Question

Find a degree 3 polynomial with real coefficients having zeros 2 and 4 - 2i and a lead coefficient of 1. Write P in expanded form.

Answer 1

Since 4 - 2i is a zero, 4 + 2i is also a zero.

x = 2, x = 4 - 2i, x = 4 + 2i

x - 2 = 0, x - 4 + 2i = 0, x - 4 - 2i = 0

P(x) = (x - 2)(x - 4 + 2i)(x - 4 - 2i)

P(x) = (x - 2)(x² - 8x + 20)

P(x) = x³- 10x² + 36x - 40