SOLUTION: n=3; 2+5i; f(1)=104

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Question 840044: n=3; 2+5i; f(1)=104
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
One can almost see exactly what you are asking.
f%28x%29=%28x-c%29%28x-%282%2B5i%29%29%28x-%282-5i%29%29
%28x-c%29%28%28x-2%29%2B5i%29%28%28x-2%29-5i%29
%28x-c%29%28%28x-2%29%5E2-i%5E2%2A25%29
%28x-c%29%28%28x-2%29%5E2%2B25%29
%28x-c%29%28x%5E2-4x%2B4%2B25%29
f%28x%29=%28x-c%29%28x%5E2-4x%2B29%29

Maybe need a constant factor, but do need to check for f%281%29=104 as given.

f%281%29=k%281-c%29%281-4%2B29%29=104
k%281-c%29%2826%29=104
26k%281-c%29=104
-
Let's just see what happens if k=1 and try to find a c.
26-26c=104
-26c=104-26
c=%2826-104%29%2F26
highlight%28c=-3%29
GOOD. An easy value.

ANSWER: highlight%28highlight%28f%28x%29=%28x%2B3%29%28x%5E2-4x%2B29%29%29%29