Finding the Formula for a Polynomial with imaginary roots
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Finding the Formula for a Polynomial with imaginary roots

[From: ] [author: ] [Date: 13-03-03] [Hit: ]
Thanks.Find an nth-degree polynomial function with real coefficients satisfying the given conditions.f(x) = x^3-3x^2-15x+125-Nope.One of the terms should be (x+5).The complex terms look good to me, however.......
I'm not sure I'm setting up the problem correctly. Can you please tell me if it's right? if it's not what's the correct set-up? Thanks.

Find an nth-degree polynomial function with real coefficients satisfying the given conditions.
n=3; -5 and 4+3i are zeros; f(2)=91

f(x)=a(x-6)(x-4+3i)(x-4-3i)

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(x-4)^2 = -9 for the complex roots
x^2-8x+16 = -9
(x^2-8x+25) = 0
x = -5 for the real root
(x+5) = 0
f(x) = a(x+5)(x^2-8x+25)
91 = a*7*13
a = 1
f(x) = x^3-8x^2+25x+5x^2-40x+125
f(x) = x^3-3x^2-15x+125

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Nope. One of the terms should be (x+5). The complex terms look good to me, however.
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