How to find the cubic polynomial?

Question

Find a cubic polynomial in standard form with real​ coefficients, having the given zeros.

0 and 3+5i

Answer 1

x = 0 x = 3 + 5i (x = 3 - 5i)

This polynomial function does have a conjugate pair.

x = 3 ± 5i

x - 3 = ± 5i

(x - 3)² = -25

x² - 6x + 9 = -25

x² - 6x + 34 = 0

x(x² - 6x + 34) = x³ - 6x² + 34x

P(x) = x³ - 6x² + 34x

Answer 2

Hi Jade,

Here's one way that you can approach this problem. Hopefully it helps!

Ross