Using the given zero, find all other zeros of f (x). - 2i is a zero of f (x) = x4 - 5x2 - 36

Hello:

if : - 2i the zero of f (x) then : 2i is zero ... (even function)

so : f (x) = (x-2i) (x+2i) g (x) ... g (x) = ax²+bx + c

butt : (x-2i) (x+2i) = x² - (2i) ² = x²+4 ... (i²=-1)

f (x) = (x²+4) (ax²+bx+c) = ax^4 + bx^3+cx² + 4ax² + 4bx+4c

f (x) = ax^4 + bx^3 + (c+4a) x²+4bx+4c

but : f (x) = x4 - 5x2 - 36

so:

a = 1

b=0

c+4a=-5

4c = - 36

conclusion : a = 1 b = 0 c = - 9

g (x) x²-9

g (x) = 0 : x²-9 = 0

(x-3) (x+3) = 0

x-3=0 or x+3=0

x=3 or x = - 3

all zero are : 2i, - 2i, 3, - 3