Timeline for What can be said about the roots of the polynomial $x^{n+1} - (1 - x)^n ( n + x )$?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Sep 5, 2023 at 0:26 | comment | added | shuhalo | Fun fact: if you replace $y = x/(1-x)$ in the last term, then you can rewrite the zero condition as $y^{n+1} - 2 y - n = 0$. | |
| Aug 31, 2023 at 18:19 | vote | accept | shuhalo | ||
| Aug 31, 2023 at 9:39 | comment | added | Fedor Petrov | @YCor indeed , but for any complex value $e^{n\log(x-1)+i\pi (2k+1)n}$ (with integer $k$) the proof works | |
| Aug 31, 2023 at 9:00 | comment | added | YCor | For non-integer real $n>0$ and $x>1$, it is not clear how you define $(1-x)^n$. | |
| Aug 30, 2023 at 15:00 | history | answered | Fedor Petrov | CC BY-SA 4.0 |