SOLUTION: What is the polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros 1+3i, 4+ square root of 10
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Question 558235: What is the polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros 1+3i, 4+ square root of 10 Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! What is the polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros 1+3i, 4+ square root of 10
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If 1+3i is a zero, so is 1-3i
If 4
f(x) = (x-(1+3i))(x-(1-3i))(x-(4+sqrt(10))(x-(4-(sqrt(10))
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f(x) = ((x-1)-3i))((x-1)+3i))((x-4)-sqrt(10))((x-4)+sqrt(10))
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f(x) = [(x-1)^2+9][(x-4)^2-10]
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f(x) = [x^2-2x+10]
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Multiply those 2 factors:
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Cheers,
Stan H.
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