Question 166626: Can someone help me with the question:
Use the rational zeros theorem to list all possible rational zeros of P(x)=3x^3-5x^2+4x-2.
Thank you.
Found 2 solutions by stanbon, gonzo:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Use the rational zeros theorem to list all possible rational zeros of P(x)=3x^3-5x^2+4x-2.
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Since the coefficients add to zero, x=1 is a root.
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Use synthetic division to find the other roots:
1)....3....-5,,,,4....-2
........3....-2...2...|..0
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Quotient: 3x^2-2x+2
Remainder: 0
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Find the zeroes of the Remainder, 3x^2 -2x + 2:
x = [2 +- sqrt(4 - 4*3*2)]/(2*3)
x = [2 +- sqrt(4 - 24)]/6
x = [2 +- sqrt(-20)]/6
These are not rational zeroes.
The only rational zero is x=1
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Cheers,
Stan H.
Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website! possible zeroes are plus or minus (all factors of the constant term / all factors of the leading coefficient).
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all factors of the constant term 2 are plus or minus (1,2).
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all factors of the leading coefficient 3 are plus or minus (1,3).
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all factors of the (constant term / leading coefficient) are plus or minus
[(1,2)/(1,3)].
this would be plus or minus [(1/1), (2/1), (1/3), (2/3)]
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that boils down to plus or minus [ 1, 2, 1/3, 2/3 ].
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the plus or minus is important.
it either needs to be in front of the whole group as i have shown, or it needs to be in front of each possible factor individually.
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a decent tutorial on the subject can be found here:
http://www.purplemath.com/modules/rtnlroot2.htm
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