Why doesn't ration zero theorem work on 3x^3+2x^2+4x–6
the 12 rational numbers that could possibly be zeros of P(x) are (+-)1, 2, 3, 6, 1/3, 2/3
but none of them are zeros of 3x^3+2x^2+4x–6
Appreciate for your help
note that the rational root theorem does not guarantee a rational root ... it says if a rational root exists, then it must be of the form p/q where p is a factor of the constant term and q is a factor of the leading coefficient.