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Question 120024: find all the zeros for f(x)=x to the fourth power - 6 times x to the third power + 9 times x to the second power + 6 times x - 10 if one zero is 3-i
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! find all the zeros for f(x)=x to the fourth power - 6 times x to the third power + 9 times x to the second power + 6 times x - 10 if one zero is 3-i
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f(x) = x^4 - 6x^3 + 9x^2 + 6x - 10
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If 3-i is a zero so is 3+i
Therefore (x-(3-i))(x-(3+i)) = ((x-3)+i)((x-3)+i)
= (x-3)^2+1 = x^2-6x+10 is a factor of f(x)
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Using long division find the other factor(s):
The quotient is x^2-1, so the other zeroes are x=1 and x=-1
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All the zeroes: 3-i,3+i,1,-1
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Cheers,
Stan H.
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