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put this solution on YOUR website!Find the polynomial function of degree 3 with the given numbers as zeros:
1 - SqRt(3),
1 + SqRt(3),
-2
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The given 0,s also represent 3 factors of the function:
The last one, -2 is (x+2), right?
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Regarding the other two, think of the doing completing the square in reverese:
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x = 1 - SqRt(3)
x - 1 = -Sqrt(3)
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Square both sides:
(x-1)^2 = -SqRt(3)* -SqRt(3), same as squaring +SqRt(3)
x^2 - 2x + 1 = 3
x^2 - 2x + 1 - 3 = 0
x^2 - 2x - 2 = 0
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Mult the two factors:
(x+2)* (x^2 - 2x - 2) = (x^3 - 4x^2 + 2x + 4) is the function with the given 0's
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