Question 166626
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.