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This work is intended to present contributions to solve problems which occur in the application of iterative methods for solving polynomial equations, thus amplifying the numerical computational means already available. We present two new techniques, called Initial Pha se and Variant of the Initial Phase, in chapter 2, by means o f which we determine one or more initial approximations to the root of the smaller modulus of a polynomi al equation. In chapter 3 of this work, a new iterative method, called MIDREM is proposed. This method gives not only the root of a polynomial equation but also its multiplicity. Considerations about Graeffe's method to solve real polynomial equations are presented in chapter 4. It is well known that this method has been considered inadequate for computational purposes due to the frequent occurrence of overflows. | Our proposed programme avoids this inconvenience and makes the method computationally efficient.