SOLUTION: Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing​ utility, use it to graph the function and v

Algebra ->  Rational-functions -> SOLUTION: Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing​ utility, use it to graph the function and v      Log On


   

Question 1074598: Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing​ utility, use it to graph the function and verify the real zeros and the given function value.
n=3
4 and 2i are zeroes
f(1)=30
Found 2 solutions by Fombitz, Alan3354:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rational coefficients means that complex roots come in complex conjugate pairs.
f%28x%29=a%28x-4%29%28x-2i%29%28x%2B2i%29
f%28x%29=a%28x-4%29%28x%5E2%2B4%29
So,
f%281%29=a%281-4%29%281%5E2%2B4%29=30
a%28-3%29%285%29=30
-15a=30
a=-2
So,
f%28x%29=-2%28x-4%29%28x%5E2%2B4%29
f%28x%29=-2x%5E3%2B8x%5E2-8x%2B32

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 satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value.
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If 2i is a zero, then -2i is also.
---
--> (x-4)*(x-2i)*(x+2i) = 0
(x-4)*(x^2+4) = 0
f(x) = x^3 - 4x^2 + 4x - 16
----
f(1) = 1 - 4 + 4 - 16 = -15
Multiply by -2
--> f(x) = -2x^3 + 8x^2 - 8x + 32