Question

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

-2i is a zero of f(x) = x4 - 45x2 - 196

Answer 1

x = -2i or x = 2i

x^2 = (-2i)^2 or x^2 = (2i)^2

x^2 = 4i^2 or x^2 = 4i^2

x^2 = 4i^2

x^2 = 4(-1)

x^2 = -4

x^2 + 4 = 0

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so if -2i is a zero, then x^2 + 4 is a factor

Answer 2

what this allows you to do is divide x^4 - 45x^2 - 196 by x^2 + 4 using polynomial long division to find the other other factors, which leads you to the other roots

Answer 3

let me know if you need me to go over the polynomial long division

Answer 4

Yes, please.

Answer 5

ok first set it up like so