G(a)=g(b)=0. The existence of ξ∈(a, b) makes g'(ξ)=0, where ξ is neither a nor b, so if g'(a)=0 is added, there will be no repetition.

Similarly, L0-1zeros Q_i of g' constructed from l0 zeros P_i of g does not duplicate the original p _ i.