Question

Write a polynomial function to the least degree with theese roots 2 &3i

Answer 1

At least what degree does it have to be?

Answer 2

my guess is 3

Answer 3

yeah i would be three

Answer 4

It would be three since it say "to the least degree".

Set up your factors as (x-2)(x-3i)(x+3i) and mutiply out.

Hint: (x-ai)(x+ai) = x^2 + a^2

Answer 5

¿Wouldn't it simply be (x-2)(x-3i)? It doesn't ask for the polynomial to have real coefficients.

Answer 6

@Krebante - Technically, you are correct. There was an assumption made as to the class/section the question came from. This type of problem is very typical when a student learns that complex factors come in conjugate pairs.

Unless @Pie_Boi is taking a class on complex polynomials (which I've never seen, heard of, nor can imagine *why* you'd study them), I'm fairly confident that the coefficients were assumed to be real and the degree they (the question writers) were looking for was 3.