Question

can anyone explain to me in which cases and why Descartes' rule of signs for determining the number of real and imaginary roots of an equation is not applicable?

Answer 1

Descartes' rule of signs-a technique for determining the number of positive or negative real roots of a polynomial.
The rule gives us an upper bound number of positive or negative roots of a polynomial. It is not a complete criterion, i.e. it does not tell the exact number of positive or negative roots.

Answer 2

All here
http://en.wikipedia.org/wiki/Descartes%27_rule_of_signs

Answer 3

good worked out examples here too
http://www.purplemath.com/modules/drofsign.htm