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The purpose of this dissertation is to discuss constructive processes of the "Fundamental Theorem of Algebra", mainly the iterative method of Nickel, [11], which converges for any initial value and for any degree of the polynomial. This method can be applied to polynomials with real or complex coefficients. By successive applications of this method, a11 roots can be obtained. Ihe Nickel method is based on a paper from Nasitta[1],which gives a general method to obtain zeroes of analytic functions. Nickel improved the Nasitta method, bringing it into a suitable fashion for polynomials