Question

Find a polynomial function with real coefficients that has the given zeros. (There are many correct answers.)
4, −3i

Answer 1

(x-4)(x^2+9) would work

Answer 2

simplifies to x^3-4x^2+9x-36

Answer 3

How did you get that? :) I mean, I know that (x-4) would a factor, (x+3i), and (x-3i)?

Answer 4

Not too sure about the last one.

Answer 5

well (x-4) is a factor. now if you multiplied (x-3i) and (x+3i) you get (x^2+9) which has real coefficients and that is what we want. now simplify, multiply (x-4)(x^2+9) and you get x^3-4x^2+9x-36.

Answer 6

x^3-4x^2+9x-36=0 has 4,-3i and 3i as solutions

Answer 7

Ah, I see. :) So, I was right?

Answer 8

yea

Answer 9

Thank you.

Answer 10

np