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We study least deviation of logarithmic derivatives of real-valuedpolynomials with a fixed root from zero on the segment $[-1;1]$ in the uniformnorm with the weight $\sqrt{1-x^2}$ and without it. Basing on results ofKomarov and Novak and on a certain determinant identity due to Borchardt, wealso establish a criterion for best uniform approximation of continuousreal-valued functions by logarithmic derivatives in terms of a Chebyshevalternance.

Logarithmic Derivatives of Least Deviation from Zero