Topological complexity and Schwarz genus of general real polynomial equation

We prove that the minimal number of branchings of arithmetic algorithms of approximate solution of the general real polynomial equation $x^d+a_1x^{d-1}+\dots+a_{d-1}x+a_d=0$ of odd degree $d$ grows to infinity at least as $\log_2d$. The same estimate is true for the $\varepsilon$-genus of the real algebraic function associated with this equation, i.e. for the minimal number of open sets covering the space $\mathbb R^d$ of such polynomials in such a way that on any of these sets there exists a continuous function whose value at any point $(a_1,\dots,a_d)$ is approximately (up to some sufficiently small $\varepsilon>0$) equal to one of real roots of the corresponding equation.