SOLUTION: find an nth degree polynomial function with real coefficient satisfying the given conditions: n=4 and i and 4 i are zeros; f(-1)=68

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Question 820370: find an nth degree polynomial function with real coefficient satisfying the given conditions: n=4 and i and 4 i are zeros; f(-1)=68
Found 2 solutions by ewatrrr, stanbon:
Answer by ewatrrr(24785) (Show Source):
You can put this solution on YOUR website!

Hi,
find an nth degree polynomial function with real coefficient satisfying the given conditions:
n=4 and i and 4 i are zeros; f(-1)=68
f(x) = a(x-i)(x+i)(x+4i)(x-4i)
f(x) = a(x^2+1)(x^2 + 4)
f(-1) = 68 = a(2)(5), a = 6.8
f(x) = 6.8(x^2+1)(x^2 + 4)

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
find an nth degree polynomial function with real coefficient satisfying the given conditions: n=4 and i and 4 i are zeros; f(-1)=68
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Zeros:: +-i ; +-4i
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f(x) = a(x^2+1)(x^2+16)
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Solve for "a":
f(-1) = a(1+1)(1+16) = 34a
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Solve:
34a = 68
a + 2
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Ans: f(x) = 2(x^4+17x^2+16)
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Cheers,
Stan H.