SOLUTION: Find an nth- degree polynomial function with real coefficients satisfying the given conditions. n=3 3 and 5i are zeros f(-1) = -312 F(x)=

Question 1178029: Find an nth- degree polynomial function with real coefficients satisfying the given conditions.
n=3
3 and 5i are zeros
f(-1) = -312
F(x)=
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Real coefficients with roots 3 and 5i means -5i is another root. Since the polynomial is degree 3, those are the only roots.

The linear factor corresponding to the root 3 is (x-3); the quadratic factor corresponding to the roots 5i and -5i is (x^2+25).

So f(x) is of the form

Determine the constant a knowing that f(-1)=-312:

The function is

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