Geodesic
On Arrangements of Real Roots of a Real Polynomial and Its Derivatives
Serdica Mathematical Journal, Tome 29 (2003) no. 1, pp. 65-74.

Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library

We prove that all arrangements (consistent with the Rolle theorem and some other natural restrictions) of the real roots of a real polynomial and of its s-th derivative are realized by real polynomials.
Keywords: Arrangement of Roots 
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Kostov, Vladimir. On Arrangements of Real Roots of a Real Polynomial and Its Derivatives. Serdica Mathematical Journal, Tome 29 (2003) no. 1, pp. 65-74. http://geodesic.mathdoc.fr/item/SMJ2_2003_29_1_a5/