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In the article we develop Euler-Lagrange method and calculate all the rootsof an arbitrary complex polynomial $P(z)$ on the base of calculation (similarto the Bernoulli-Aitken-Nikiporets methods) of the limits of ratios of Hadamarddeterminants built by means of coefficients of expansions into Taylor andLaurent series of the function~$\frac{P'(z)}{P(z)}$.

Hadamard and Vandermonde determinants and Bernoulli-Euler-Lagrange-Aitken-Nikiporets type numerical method for roots of polynomials