Question

Can someone help me with this?? I'm getting confused with the i's.

Write a polynomial of the smallest degree with roots 6, 3i and -3i.

Answer 1

use sum and product for the conjugate roots

Answer 2

then you will get a quadratic facotr and a linear factor

Answer 3

Is this the right direction -
(x-6) (x-3i) (x-(-3i)

Answer 4

sum 3i-3i=0

product 3ix-3i=9

quadratic factor = x^2-Sx+P
x^2-0x+9
x^2+9 is ur quadratic factor

Answer 5

(x-6)(x^2+9)

Answer 6

then expand

Answer 7

Thanks! I think I got it: x^3-6x^2+3x-54=0