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

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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 
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/
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     title = {On {Arrangements} of {Real} {Roots} of a {Real} {Polynomial} and {Its} {Derivatives}},
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