{"title":"多项式函数等像对的极限行为","authors":"Peter M. Higgins","doi":"10.1080/07468342.2023.2237854","DOIUrl":null,"url":null,"abstract":"AbstractFor any polynomial p(x) with real coefficients and of degree n≥1, for sufficiently large positive x there is a unique y, distinct from x, such that p(x) and p(y) are equal in absolute value. We show that, in the limit, the mean of x and y is equal to the mean of the roots of p(x).","PeriodicalId":38710,"journal":{"name":"College Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Limiting Behaviour of Pairs with Equal Images for Polynomial Functions\",\"authors\":\"Peter M. Higgins\",\"doi\":\"10.1080/07468342.2023.2237854\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"AbstractFor any polynomial p(x) with real coefficients and of degree n≥1, for sufficiently large positive x there is a unique y, distinct from x, such that p(x) and p(y) are equal in absolute value. We show that, in the limit, the mean of x and y is equal to the mean of the roots of p(x).\",\"PeriodicalId\":38710,\"journal\":{\"name\":\"College Mathematics Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-08-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"College Mathematics Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/07468342.2023.2237854\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Social Sciences\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"College Mathematics Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/07468342.2023.2237854","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Social Sciences","Score":null,"Total":0}
Limiting Behaviour of Pairs with Equal Images for Polynomial Functions
AbstractFor any polynomial p(x) with real coefficients and of degree n≥1, for sufficiently large positive x there is a unique y, distinct from x, such that p(x) and p(y) are equal in absolute value. We show that, in the limit, the mean of x and y is equal to the mean of the roots of p(x).
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