I'm wondering... Do you think that your algorithm can find the roots of a 
polynomial like

p(x) = x^4 - 4x^3 + 6x^2 - 4x + 1 ?

This is an easy one : it has only one root (x=1) of multiplicity 4. And 
since p(x) >= 0, i can't see how your algorithm would apply here.

Fran