Find polynomial function

Question

Find a polynomial function P of the lowest possible​ degree, having real​ coefficients, a leading coefficient of​ 1, and with the given zeros.

3+2i​, −1​, and 2

Answer 1

x = 3 + 2i​ (x = 3 - 2i) x = −1​ x = 2

The polynomial function does come in conjugate pairs. Find the factors for each zero.

x - 3 = ± 2i x = -1 x = 2

(x - 3)² = -4 x + 1 = 0 x - 2 = 0

x² - 6x + 9 = -4

x² - 6x + 13 = 0

(x + 1)(x - 2)(x² - 6x + 13) = (x² - 2x + x - 2)(x² - 6x + 13)

= (x² - x - 2)(x² - 6x + 13)

= x⁴ - 6x³ + 13x² - x³ + 6x² - 13x - 2x² + 12x - 26

= x⁴ - 7x³ + 17x² - x - 26

P(x) = x⁴ - 7x³ + 17x² - x - 26