A class of globally monotonically convergent iterative methods for the determination of zeros of a polynomial is presented. The proposed method uses the well-known Newton’s second order method as a basic ingredient to generate this class of methods following the approach of Petkovic and Trickovie as supported by Cauchy Schwartz inequality from which come in hand three methods of fourth order. The obtained methods can be used to provide tight inclusion conditioning bounds separating the sought zeros. This may always provide good numerical approximations within the theoretical conditioning bounds. It is found that one of the fourth order methods so obtained competes most favourably with any known methods for finding zeros of a polynomial.