SOLUTION: Please help me find a third-degree polynomial equation with rational coefficients that has roots -4 and 2+i.

Question 1034313: Please help me find a third-degree polynomial equation with rational coefficients that has roots -4 and 2+i.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Please help me find a third-degree polynomial equation with rational coefficients that has roots -4 and 2+i.
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Roots are -4, 2+i, 2-i
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f(x) = (x+4)((x-2)-i)((x-2)+i)
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f(x) = (x+4)((x-2)^2 +1)
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f(x) = (x+4)(x^2 - 4x +5)
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f(x) = x^3 -4x^2 + 4x^2 + 5x - 16x + 20
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f(x) = x^2 - 11x + 20
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Cheers,
Stan H.
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