Precalc
posted by James on .
Use the given zero to find the remaining zeros of the function:
h(x)=x^415x^3+55x^2+155x1476 Zero:54i
I multiplied [x(54i)][x(5+4i)] and got x^210x+9.
The example I have says to divide that by h and get a second quadratic equation that is also a factor of h. I have to use that equation to find the remaining zeros. How do I find the second equation?

(x(54i))(x(5+4i))
= (x5+4i)(x5  4i)
= x^2  5x  4ix  5x + 25 + 20i + 4ix 20i  16i^2
= x^2  10x + 41
now divide x^415x^3+55x^2+155x1476 by x^2  10x + 41 to get
x^2  5x  36
(Google " long algebraic division" if you don't know how to do that)
now solving this quadratic:
x^2  5x  36 = 0
(x9)(x+4) = 0
x = 9, or x = 4