Higgins, Peter (2023) Limiting behaviour of pairs with equal images for polynomial functions. College Mathematics Journal, 54 (4). pp. 391-393. DOI https://doi.org/10.1080/07468342.2023.2237854
Higgins, Peter (2023) Limiting behaviour of pairs with equal images for polynomial functions. College Mathematics Journal, 54 (4). pp. 391-393. DOI https://doi.org/10.1080/07468342.2023.2237854
Higgins, Peter (2023) Limiting behaviour of pairs with equal images for polynomial functions. College Mathematics Journal, 54 (4). pp. 391-393. DOI https://doi.org/10.1080/07468342.2023.2237854
Abstract
For any non-constant polynomial p(x) with real coefficients, for all sufficiently large x there is a unique y, distinct from x, such that p(x) and p(y) are equal in absolute value. We prove that, in the limit, the mean of x and y is equal to the mean of the roots of p(x).
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | polynomials, roots, limits |
| Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
| SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
| Depositing User: | Unnamed user with email elements@essex.ac.uk |
| Date Deposited: | 20 Sep 2023 18:22 |
| Last Modified: | 18 Oct 2023 13:33 |
| URI: | http://repository.essex.ac.uk/id/eprint/35767 |
Available files
Filename: CollMathJ-D-22-00202_R1 (11).pdf
Licence: Creative Commons: Attribution-Noncommercial 4.0
Embargo Date: 27 September 2024