Question

15 Points!

Using the given zero, find all other zeros of f(x).

-2i is a zero of f(x) = x4 - 32x2 - 144

A) 2i, 12, -12

B) 2i, 6i, -6i

C) 2i, 6, -6

D) 2i, 12i, -12i

Answer 1

`f(x)=x^4-32x^2-144\\\\f(x)=0\iff x^4-32x^2-144=0\\\\x^4-36x^2+4x^2-144=0\\\\x^2(x^2-36)+4(x^2-36)=0\\\\(x^2-36)(x^2+4)=0\iff x^2-36=0\ \vee\ x^2+4=0\\\\x^2=36\ \vee\ x^2=-4\\\\x=\pm√(36)\ \vee\ x=\pm√(-4)\\\\x=-6\ \vee\ x=6\ \vee\ x=-2i\ \vee\ x=2i`

Answer: C) 2i, 6, -6

Answer 2

Replace f(x) with 0 and swith the equation around to solve for x

x^4 - 32x^2 - 144 = 0

Factor the left side:

(x+6) (x-6) (x^2+4)

so far we have x+6 = 0, x = -6
x -6 = 0, x = 6

solve x^2 +4 = 0
x^2 = -4
x = sqrt(-4)
x = 2i, -21

The answer is B) 2i, 6, -6