Write a polynomial P in lowest degree given the following roots: -2, 8, 2i, 1-i

Question

Write a polynomial P in lowest degree given the following roots: -2, 8, 2i, 1-i

Answer 1

Kaylene, if you know the roots (what makes the function equal zero) and you know the degree, then you can create the polynomial ,

Example: if the roots are 1, 2, 3 and the degree is 3, then you have

p(x) = (x - 1)(x - 2)(x - 3)

Example: if the roots are 1, 2, 3 and the degree is 4, then you have

p(x) = (x - 1)(x - 2)(x - 3)² or p(x) = (x - 1)²(x - 2)(x - 3) or p(x) = (x - 1)(x - 2)²(x - 3)

There is a difference if imaginary numbers are involved--see below with Paul's answer. Hope this helps, but please let me know--Andrew

Answer 2

This is a 6th degree polynomial because complex roots of a polynomial with real coefficients occur in conjugate pairs, i.e.

if a+bi is a root so is a-bi.