SOLUTION: Find the zeroes of f(x) = x^4-x^3-4x^2+4x. thanks in advance

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Question 188390: Find the zeroes of f(x) = x^4-x^3-4x^2+4x.

thanks in advance

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the zeroes of f(x) = x^4-x^3-4x^2+4x
x^4-x^3-4x^2+4x = 0
Factor:
x(x^3-x^2-4x+4) = 0
x = 0 is one of the zeroes.
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Since the coefficients of x^3-x^2-4x+4 add up zero, x=1 is a zero.
Use synthetic division to find the other zeroes:
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1)....1....-1....-4....4
.......1.....0.....-4..|..0
The remaining factor is x^2-4 which
factors as (x-2)(x+2).
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So, the four zeroes are x= 0 or x=1 or x = 2 or x=-2
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Cheers,
Stan H.