SOLUTION: Find an nth degree polynomial function with real coefficients, a leading coefficient of 1 and satisfying the given conditions n=3 -5 and 2+5i are zeros

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Question 1200976: Find an nth degree polynomial function with real coefficients, a leading coefficient of 1 and satisfying the given conditions n=3 -5 and 2+5i are zeros
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


If the coefficients of the polynomial are real and 2+5i is a root, then 2-5i is also a root.

So the three roots are
-5
2+5i
2-5i

and the polynomial is

f%28x%29=a%28x-%28-5%29%29%28x-%282%2B5i%29%29%28x-%282-5i%29%29

where a can be any constant.

%28x-%28-5%29%29=%28x%2B5%29





ANSWER: f%28x%29=a%28x%5E3%2Bx%5E2%2B9x%2B145%29

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find an nth degree polynomial function with real coefficients, a leading
coefficient of 1 and satisfying the given conditions n=3 -5 and 2+5i are zeros
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A correction to the post by @greenestamps. 

    Since the leading coefficient is 1 (one), as it is given,

    the polynomial is  f(x) = x^3 + x^2 + 9x + 145.    ANSWER

Solved.