SOLUTION: Find an nth degree polynomial function with real coefficients satisfying the given conditions. n=4 2i and 5i are zeros F(-1)=130 F(x)=

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Question 1177978: Find an nth degree polynomial function with real coefficients satisfying the given conditions.
n=4
2i and 5i are zeros
F(-1)=130
F(x)=
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
n=4
x%5B1%5D=2i=> you also have x%5B2%5D=-2i
x%5B3%5D=5i => you also have x%5B4%5D=-5i

F%28x%29=a%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29
F%28x%29=a%28x-2i%29%28x%2B2i%29%28x-5i%29%28x%2B5i%29
F%28x%29=a%28x%5E4+%2B+29+x%5E2+%2B+100%29

since given F%28-1%29=130, use x=-1 and F%28x%29=130 to calculate the value of a
130=a%28%28-1%29%5E4+%2B+29+%28-1%29%5E2+%2B+100%29
130=a%281+%2B+29+%2B+100%29
130=a%28130%29
a=1
and your equation is
F%28x%29=x%5E4+%2B+29+x%5E2+%2B+100