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

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) (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

where a can be any constant.

ANSWER:

Answer by ikleyn(52788) (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
~~~~~~~~~~~~~~~~~~~~~~~

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.

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