Linear recurrent sequences and polynomial roots

We consider the problem of the determination of the largest modulus of a root of a complex polynomial P. We obtain lower and upper bounds using properties of appropriate linear recurrent sequences associated with P. This allows giving the absolute value of a dominant root as the limit as in Bernoulli’s process. We finally discuss a rule of Jacobi in his refinement of Bernoulli’s method. Relevant examples are obtained through pari and maple procedures.