SOLUTION: Find the 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 rea

Algebra ->  Rational-functions -> SOLUTION: Find the 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 rea      Log On


   

Question 1024461: Find the 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; -2 and 5+4i are zeros; f (-1)=52
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Since one of the roots is complex and it has real coefficients, the complex conjugate is also a root.
f%28x%29=a%28x%2B2%29%28x-%285%2B4i%29%29%28x-%285-4i%29%29
f%28x%29=a%28x%2B2%29%28x%5E2-10x%2B41%29
When x=-1
f%28-1%29=a%28-1%2B2%29%28-1%5E2%2B10%2B41%29
52=a%281%29%2852%29
a=1
So then,
f%28x%29=%28x%2B2%29%28x%5E2-10x%2B41%29
f%28x%29=x%5E3-8x%5E2%2B21x%2B82
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