Suppose I have an equationf(x) = x^6-x^3+2x^2-3x-1 = 0. How to determine the EXACT number of real roots in this equation? I can say from Descarte's rule of sign that f(x) has 1 negative real root and 1 or 3 positive real roots. But how can I know the EXACT number of real roots?

Not only this one, I am having problem with many other equations as well. So I want a general method which will work for all algebraic equations.

Thanks in advance.