Perturbation theorems for estimating magnitudes of roots of polynomials

Two additional new theorems are posed and proven to estimate the magnitudes of roots of polynomials. Perturbation theory and the order of magnitude of terms are employed to develop the theorems. The theorems may be useful to estimate the order of magnitudes of the roots of a polynomial a priori before solving the equation. The theorems are developed for two special classes of polynomials of arbitrary order with their coefficients satisfying certain conditions. Numerical applications of the theorems are presented as examples. It is shown that the theorems produce good estimates for the magnitudes of roots.