Question

PLEASE HELP!!!

Which of the following is a polynomial with roots -2, -3i, and 3i ?

a.) x3 + 4x2 + 9x + 24
b.) x3 - 4x2 + 9x - 24
c.) x3 + 2x2 + 9x + 18
d.) x3 - 2x2 + 9x - 18

Answer 1

so, you have the roots
x = -2
x= -3i
x = 3i

so that means,
x+2 = 0
x+3i = 0
x-3i = 0

so (x+2)(x+3i)(x-3i) =0
there's your polynomial, expand the roots

Answer 2

another way to do it is from

x = -2
x = -3i
x = 3i

you simplify by squaring those complex roots

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

so the roots would be

x = -2
x^2 = 3
x^2 = -3

so the factored form is (x + 2)(x^2 - 3)(x^2 + 3)

whichever you think looks easier

Answer 3

i got c as the answer