We consider the set of monic real univariate polynomials of a given degree $d$ with non-vanishing coefficients, with given signs of the coefficients and with given quantities of their positive and negative roots (all roots are distinct). For $d=6$ and for signs of the coefficients $(+,-,+,+,+,-,+)$, we prove that the set of such polynomials having two positive, two negative and two complex conjugate roots, is not connected.
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