SOLUTION: How can i find the third-degree polynomial equation with rational coefficients that have the given number of roots of 3,2-i? Please and thank you!
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Question 434938: How can i find the third-degree polynomial equation with rational coefficients that have the given number of roots of 3,2-i? Please and thank you! Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! How can i find the third-degree polynomial equation with rational coefficients that have the given number of roots of 3,2-i?
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If the coefficients are rational, 2+i must also be a root.
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Equation:
f(x) = (x-3)(x-(2-i))(x-(2+i))
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f(x) = (x-3)((x-2)+i)((x-2)-i)
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f(x) = (x-3)((x-2)^2+1)
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f(x) = (x-3)(x^2-4x+5)
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f(x) = x^3-4x^2+5x-3x^2+12x-15
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f(x) = x^3-7x^2+17x-15
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Cheers,
Stan H.
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