SOLUTION: Please help! I am having difficulty with this problem: Find an nth degree polynomial function with real coefficients satifying the given conditions: n=3; 4 and 2i are zeros;

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help! I am having difficulty with this problem: Find an nth degree polynomial function with real coefficients satifying the given conditions: n=3; 4 and 2i are zeros;       Log On


   



Question 395661: Please help! I am having difficulty with this problem:
Find an nth degree polynomial function with real coefficients satifying the given conditions:
n=3; 4 and 2i are zeros; f(-1)=-50
Thank you so much for any help!

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find an nth degree polynomial function with real coefficients satifying the given conditions:
n=3; 4 and 2i are zeros;
Complex solutions occur in conjugate pairs, so -2i is also a zero.
f(n) = (n-3)(n-4)(n-2i)(n+2i)
f%28n%29+=+%28n%5E2-7n%2B12%29%2A%28n%5E2+%2B+4%29
Multiply those, that's the function.
---------------------
f(-1) = 100
Multiply by -1/2
f%28n%29+=+%28-1%2F2%29%2A%28n%5E2-7n%2B12%29%2A%28n%5E2+%2B+4%29
f(-1)=-50