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Question 205164: Could someone please help me out with this problem; which are the possible rational roots of x^3-4x^2+2x+1=0? using the synthetic substitution, which of the possible rational roots is actually a root of the equation?
My brains dont seem to work right when it comes to roots =(
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Could someone please help me out with this problem; which are the possible rational roots of x^3-4x^2+2x+1=0? using the synthetic substitution, which of the possible rational roots is actually a root of the equation?
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If p/q is a rational root of this polynomial, p is and factor of 1 and q
is a factor of 1.
So the only rational roots possible are x = 1 and x = -1.
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Checking:
If x = 1 you get 1-4+2+1 = 0
Since 1 is a zero of the polynomial is a root of the polynomial.
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If x = -1 you get -1-1-2+1 which is not zero
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The only rational root is x = 1
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Cheers,
Stan H.
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