Descartes rule of Signs

For any polynomial f(x) = 0,

The maximum number of positive real roots of a equation is the number of changes of signs from positive to negative and negative to positive in f(x).

The maximum number of negative real roots of a equation is the number of changes of signs from positive to negative and negative to positive in f(-x).

Remaining roots are imaginary. 

f(x) = a*x^3 + b*x^2 – c*x + d = 0

         +         +            -         +

       Thus, we have two sign changes. Hence there are at most two positive roots.

f(-x) = -a*x^3 + b*x^2 + c*x + d = 0

           -           +            +        +

       Thus, we have one sign change. Hence there is at most one negative root.