SOLUTION: find an nth degree polynomial function with real coefficients satisfying the given conditions: n=3; 2 and 5i are zeros; f(-1)=156.

Question 255669: find an nth degree polynomial function with real coefficients satisfying the given conditions: n=3; 2 and 5i are zeros; f(-1)=156.
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
n=3; We need a third degree polynomials with the following given zero's: 2 and 5i are zeros; f(-1)=156.
Since these are solutions
x = 2 ; x = 5i. Since imaginaries travel in pairs, the other answer is x= -5i.
We have (x-2)(x-5i)(x+5i) = 0
Now,
f(-1) = (-1-2)(-1-5i)(-1+5i) = 156.
f(-1) = (-3)(26) = -78.
But -78 x -2 = 156, so our polynomial becomes

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