Timeline for Is there a critical point of a polynomial $f$ within every disc having as diameter the line segment between two zeros of $f$?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Feb 21, 2016 at 19:05 | vote | accept | Andreas Rüdinger | ||
| Feb 21, 2016 at 17:37 | comment | added | Will Sawin | @AndreasRüdinger Yes, this is clear, as the roots and critical points depend continuously on the value of a complex polynomial. | |
| Feb 21, 2016 at 17:28 | comment | added | Andreas Rüdinger | Thank you, you are right. However, I wanted $f$ also to be generic in the sense that $f'$ has pairwise distinct zeros (which I didn't say in the question; I will edit it accordingly). Perhaps a slight modification of your answer will still give a counterexample. | |
| Feb 21, 2016 at 17:14 | history | answered | Lev Borisov | CC BY-SA 3.0 |