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this paper presents the proposed method of assessing the roots of nonlinear algebraic equations with positive coefficients for the case of a significantly different module roots, among which there is at least one pair of complex-conjugate. The method is based on the use of the concepts of frequency and Q-factor of the roots. The obtained results could be widely adopted in the analysis and optimization of automatic control systems, wideband and pulse amplifiers, active filters, mechanical resonance systems, etc.

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а lot of tasks related with control systems analysis settled by root evaluating. This paper contains the author's opinion about estimating the systems lowest frequency complex conjugate poles. The proposed method uses the characteristic equation coefficients values to sum up the frequency and q-factor of complex conjugate poles. Based on Routh-Hurwitz stability criterion this evaluating way is applicable to free degree characteristic equation. The proposed method has been tested and endorsed by comparison with the test simulation and physical model experiments for a few common cases.