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On a new simple discriminant inequality

Aurelien Gribinski
arXiv: Classical Analysis and ODEs
Jul 2019
摘要
We prove a simple though nontrivial inequality involving a real-rooted polynomial, its successive derivatives and their discriminants. In particular we get the new inequality : $ \Dis(p-tp')>\Dis(p) $ for a polynomial $p$, its derivative $p'$ and t any non zero real. We also formulate a well-motivated conjecture generalizing our main result.
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