SOLUTION: find an nth-degree polynomial function with real coefficients satisfying the given conditions. if you are using a graph utility, use it to graph the function and verify the functio

Algebra ->  Rational-functions -> SOLUTION: find an nth-degree polynomial function with real coefficients satisfying the given conditions. if you are using a graph utility, use it to graph the function and verify the functio      Log On


   

Question 362611: find an nth-degree polynomial function with real coefficients satisfying the given conditions. if you are using a graph utility, use it to graph the function and verify the function and verify the real zeroes and the given function value......
n=3;1 and 5i are zeros;f(-1)= -104
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
If x=5i is a root, then x=-5i is also a root since complex solutions always occur as complex conjugate pairs.
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f%28x%29=a%28x-1%29%28x-5i%29%28x%2B5i%29
f%28x%29=a%28x-1%29%28x%5E2%2B25%29
f%28-1%29=a%28-1-1%29%281%2B25%29
-104=a%28-2%29%2826%29
a=2
f%28x%29=2%28x-1%29%28x%5E2%2B25%29
f%28x%29=2%28x%5E3-x%5E2%2B25x-25%29
highlight%28f%28x%29=2x%5E3-2x%5E2%2B50x-50%29