Question

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

Answer 1

@John_ES

Answer 2

you know it looks like
\[(x+2i)(x-2i)(something)\] or
\[(x^2+4)(something)\]
find the "something" by division

Answer 3

complex zeros always occur in pairs.

Answer 4

or factor:
\[ x^4 - 5x^2 - 36
=(x^2+4)(x^2-9)\]

Answer 5

you didn't have to be told any zeros for this one to find all of them
it is a quadratic in \(x^2\)

Answer 6

i wanted to say if -2i is a zero then +2i is also a zero

Answer 7

I would follow @satellite73 indication, if -2i is a zero, then +2i is also a zero. Then, from this, I would divide,
\[(x^4-5x^2+36)/(x^2+4)=x^2-9\]
Then factorize it,
\[x^2-9=(x+3)(x-3)\]
And you find the other solutions, +3 and -3. In total, +2i, -2i, +3 and -3.

Answer 8

Sorry it should be -36 not +36.

Answer 9

These are my choices:
2i, 6i, -6i

2i, 3i, -3i

2i, 6, -6

2i, 3, -3

Answer 10

@John_ES

Answer 11

@MandyNeedsHelp, @JohnES practically gave you the answer already.

Answer 12

@Hero i dont want your help if you're just going to be impatient.

Answer 13

I'm not being impatient. I'm just saying he made it more than obvious for you.