Question 983756
The possible roots to check are:
Plus&Minuses of 1,2,3,6,1/2,3/2;
NONE of them will give remainder of 0 when checked in synthetic division.
The coefficients p and q for possible roots p/q are from factors for p=6 and factors for q=2.


The function has ONE real root.  {{{-0.689}}} is that real root.  This would not be found using Rational Roots Theorem.  The root calculator at http://xrjunque.nom.es/Polycalc.aspx?tb1=y%3d2x^3-4x^2%2b5x%2b6&tb3=&rnd=True&frac=False&ignoreSpaces=True  was used.
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xrjunque.nom.es/rootfinder.aspx