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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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  • Junxiang Xu, 2020. "Paths of Real Roots for Odd-Degree Polynomials with Parameters," Abstract and Applied Analysis, Hindawi, vol. 2020, pages 1-21, November.
    • Handle: RePEc:hin:jnlaaa:4729872
    DOI: 10.1155/2020/4729872
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