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In the present paper, a method is proposed for adaptive estimation and tracking of roots of time-varying, complex, and univariate polynomials, e.g. z-transform polynomials that arise from finite signal sequences. The objective with the method is to alleviate the computational burden induced by factorization. The estimation is done by solving a set of linear equations; the number of equations equals the order of the polynomial. To avoid potential drifting of the estimations, it is proposed to verify with Aberth-Ehrlich's factorization method at given intervals.