Question 135276
Here is a great description of the rule --> http://www.purplemath.com/modules/drofsign.htm

Using that information. we see that if x is positive, {{{4x^3-9x^2+6x+4=0}}} has 2 changes in sign. So there are either 2 or 0 real roots.

If x is negative,  {{{4x^3-9x^2+6x+4=0}}} becomes {{{-4x^3-9x^2-6x+4=0}}}, which has one change in sign. So there is exactly one negative real root.

does this help ?