Paths of Real Roots for Odd-Degree Polynomials with Parameters

Abstract EN

In this paper, we construct a connected path of real roots of odd-degree real polynomials depending on parameters continuously, which joins with all parameters.

Moreover, most of the points on the path are odd-multiple real roots except for at most countable even-multiple real roots.

Furthermore, some geometrical features of the path can be seen easily from the construction.