Timeline for A question on the real root of a polynomial
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Feb 18, 2023 at 15:47 | history | edited | kerzol | CC BY-SA 4.0 |
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| Feb 18, 2023 at 13:55 | comment | added | Timothy Chow | If you compute more terms using the recurrence then the polynomials $f_n(x)$ seem to factor nicely; see A054142 and A145324 for example. | |
| Feb 18, 2023 at 11:47 | comment | added | kerzol | hum... You are right. Softwares are not intelligent enough to simplify stuff. The roots of $f_9$ are -$ \frac{5}{3} + \frac{2 \sqrt{7} \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{3} + \frac{\pi}{6} \right)}}{3}; - \frac{5}{3} + \frac{2 \sqrt{7} \sin{\left(\frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{3} + \frac{\pi}{6} \right)}}{3}; - \frac{5}{3} - \frac{2 \sqrt{7} \cos{\left(\frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{3} \right)}}{3}$ | |
| Feb 18, 2023 at 9:16 | comment | added | Pavel Gubkin | This looks like a calculation error of some type. $P(x) = x^4 + 7x^3 + 16x^2 + 13x + 2$ has four real zeroes | |
| Feb 18, 2023 at 9:00 | history | answered | kerzol | CC BY-SA 4.0 |