Question

Giving a medal and a fan!
using the given zero,find all the other zeroes of f(x).
-2i is a zero of f(x)=x^4-45x^2-196

Answer 1

use inverse operations and distribute property and solve

Answer 2

How?

Answer 3

well use algebra if its easier for you and you use that because it makes the problem more easier to solve

Answer 4

but what can i use to fin all the other zeroes?

Answer 5

use the zero property and solve

Answer 6

there are a couple of ways to do this problem

Answer 7

ok

Answer 8

OK,so for that,i will have to factor it,right?

Answer 9

one way is that since \(-2i\) is a zero then so is \(2i\)
that means that it must have a factor of
\[(x+2i)(x-2i)=x^2+4\] so factor it as
\[x^4-45x^2-196=(x^2+4)(something)\] and then find the zeros of the something using either the quadratic formula or by factoring it

Answer 10

(x^2+4)(x^2-49),right?

Answer 11

the other way is to view \(x^4-45x^2-196\) as a quadratic in \(x^2\)

Answer 12

yeah that does it

Answer 13

(x+7)(x-7)(x-2i)(x+2i)

Answer 14

yup

Answer 15

zeroes:-7,7,2i,-2i?

Answer 16

yes

Answer 17

Thnku very much @satellite73 :)

Answer 18

yw
you did most of the work

Answer 19

:)

Answer 20

and u 2 @herua123 :)

Answer 21

:)