Question 962337: Find a polynomial f(x) of degree 3 with real coefficients and the following zeros.
-1,-1+i
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find a polynomial f(x) of degree 3 with real coefficients and the following zeros.
-1,-1+i
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If the coefficients are Real, -1-i must also be a zero.
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f(x) = (x+1)(x-(-1+i))(x-(-1-i))
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f(x) = (x+1)((x+1)-i)((x+1)+i))
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f(x) = (x+1)((x+1)^2 + 1)
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f(x) = (x+1)(x^2+2x+2)
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f(x) = x^3 +2x^2+x^2 + 2x+2x + 2
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f(x) = x^3+4x^2+4x+2
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Cheers,
Stan H.
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