SOLUTION: Using the given zero, find all other zeros of f(x). 2-6i is a zero of f(x)=x^4-4x^3+41x^2-4x+40.

Algebra ->  Real-numbers -> SOLUTION: Using the given zero, find all other zeros of f(x). 2-6i is a zero of f(x)=x^4-4x^3+41x^2-4x+40.       Log On


   

Question 1064761: Using the given zero, find all other zeros of f(x). 2-6i is a zero of f(x)=x^4-4x^3+41x^2-4x+40.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
THESE two factors give a quadratic factor:
%28x-%282-6i%29%29%28x-%282%2B6i%29%29
%28x-2%29%5E2-36i
highlight_green%28x%5E2-4x%2B40%29.

If you peform long polynomial division (not shown) for x%5E4-4x%5E3%2B41x%5E2-4x%2B40 divided by x%5E2-4x%2B40, result will be x%5E2%2B1.

f%28x%29=%28x%5E2-4x%2B40%29%28x%5E2%2B1%29

The two other zeros are system%28-i%2Cand%2Ci%29.