Question

Using the given zero, find all other zeros of f(x). (
-2i is a zero of f(x) = x^4 - 5x^2 - 36
These are the answer choices:
(a)2i, 6i, -6i
(b)2i, 6, -6
(c)2i, 3, -3
(d)2i, 3i, -3i

Answer 1

if -2i is a zero, complex numbers come in pairs so +2i will also be a zero

Answer 2

(a+2i)(a-2i)

Answer 3

so those are 2 of the terms for sure

Answer 4

there are 2 more, since it is a 4th order polynomial

Answer 5

\[ x^4 - 5x^2 - 36=(x+2i)(x-2i)(something)=(x^2+4)(something)\] find the "something by factoring

Answer 6

or you can start by factoring
\[ x^4 - 5x^2 - 36\]

Answer 7

(x^2+4) (x-3) (x+3)

Answer 8

9 * 4 = 36
and
4 - 9 = -5

Answer 9

?

Answer 10

Yes!

Answer 11

awesome :D

Answer 12

so each of those
(x - 2i)(x +2i)(x-3) (x+3) = 0

If one of those terms is 0, then the equation is true.

Answer 13

what terms?

Answer 14

When you factor f(x) = x^4 - 5x^2 - 36 , you get
(x - 2i)(x +2i)(x-3) (x+3) = 0

for that to be true

(x-2i) = 0
or
(x+2i) = 0
or
(x-3) = 0
or
(x+3) = 0

Answer 15

so the 4 possible answers or zeros of f(x) are.....

Answer 16

Idk how could i reach the answer?

Answer 17

@DanJS