SOLUTION: use the given zero to find the remaining zeros of the function f(x) = x^3 - 3x^2 + 25x - 75; zero: 5 i

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: use the given zero to find the remaining zeros of the function f(x) = x^3 - 3x^2 + 25x - 75; zero: 5 i      Log On


   

Question 635874: use the given zero to find the remaining zeros of the function f(x) = x^3 - 3x^2 + 25x - 75; zero: 5 i
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
use the given zero to find the remaining zeros of the function f(x) = x^3 - 3x^2 + 25x - 75; zero: 5 i
----
Fact: Since the coefficients are Real, -5i is also a zero.
---
Therefore (x-5i)(x+5i) = x^2+25 must be a factor of f(x)
----
Rewrite:
x^2(x-3)+25(x-3) = 9
(x-3)(x^2+25) = 0
x = 3 or x = 5i or x = -5i
==============================
Cheers,
Stan H.