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Paths of Real Roots for Odd‐Degree Polynomials with Parameters

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  • Junxiang Xu

Abstract

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.

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Handle: RePEc:wly:jnlaaa:v:2020:y:2020:i:1:n:4729872
DOI: 10.1155/2020/4729872
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