SOLUTION: how to do you find all the zeros of the function with the given zero? givin zero: 1 minus radical 3i f(x)= 3x^3

SOLUTION: how to do you find all the zeros of the function with the given zero? givin zero: 1 minus radical 3i f(x)= 3x^3 - 4x^2 + 8x +8

Question 478033: how to do you find all the zeros of the function with the given zero?
givin zero: 1 minus radical 3i
f(x)= 3x^3 - 4x^2 + 8x +8
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
how to do you find all the zeros of the function with the given zero?
givin zero: 1 minus radical 3i
f(x)= 3x^3 - 4x^2 + 8x +8
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Since the coefficients are all Real, 1+sqrt(3)i is also a zero.
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So [(x-1)+sqrt(3)i][(x-1)-sqrt(3)i] = (x-1)^2+3
= (x^2-2x+4) is a factor.
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Divide 3x^3-4x^2+8x+8 by x^2-2x+4 to see the "other" factor.
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the other factors is 3x+2.
So the remaining zero is x = -2/3
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cheers,
Stan H.
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