Question

Find a polynomial f(x) of degree 3 that has the indicated zeros and satisfies the given condition.
-4i, 4i, 2; f(4) = -256

Answer 1

yeh simple

Answer 2

f(x) =A (x+4i)(x-4i)(x-2)

Answer 3

okay and if x=4 than it must = -256, right?

Answer 4

and that's how you find a?

Answer 5

(x+4i)(x-4i) = x^2 - (-16) = x^2 +16

Answer 6

f(x) = A (x^2 +16)(x-2)

Answer 7

when x=4, f= -256

Answer 8

-256 = 32(2) A

Answer 9

A= -4

f(x) = -4 ( x^2+16)(x-2)

Answer 10

Oh I see what I did wrong, I added a negative sign by accident, thanks once again!