SOLUTION: Find a polynomial f(x)with real coefficients having the given degree and zeros Degree 5 zeros 9;-i;-6+i

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Question 772260: Find a polynomial f(x)with real coefficients having the given degree and zeros
Degree 5 zeros 9;-i;-6+i
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The complex nonreal numbers come with their conjugates.
Form the factored form of the function:
f%28x%29=%28x-9%29%28x-%28-i%29%29%28x-i%29%28x-%28-6%2Bi%29%29%28x-%28-6-i%29%29
Fully multiply the expression...
...you may need some pre-simplifications first as well as later...
f%28x%29=%28x-9%29%28x%2Bi%29%28x-i%29%28x%2B6-i%29%28x%2B6%2Bi%29
f%28x%29=%28x-9%29%28x%5E2-i%5E2%29%28%28x%2B6%29-i%29%28%28x%2B6%29%2Bi%29
f%28x%29=%28x-9%29%28x%5E2%2B1%29%28%28x%2B6%29%5E2-i%5E2%29
.
.
There is much more multiplying and simplifying to do, but at least I showed enough of the steps so you can see how to handle the complex roots and complex factors and begin their simplifications. I post just that unfinished solution to the extent shown.