{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T03:04:28Z","timestamp":1760151868422,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,4,20]],"date-time":"2022-04-20T00:00:00Z","timestamp":1650412800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11871379"],"award-info":[{"award-number":["11871379"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Key project of  National Natural Science Foundation  of Guangdong Province Universities","award":["2019KZDXM025"],"award-info":[{"award-number":["2019KZDXM025"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Split quaternions are noncommutative and contain nontrivial zero divisors. Generally speaking, it is difficult to solve equations in such an algebra. In this paper, by using the roots of any split quaternions and two real nonlinear systems, we derive explicit formulas for computing the roots of x2+bx+c=0 in split quaternion algebra.<\/jats:p>","DOI":"10.3390\/axioms11050188","type":"journal-article","created":{"date-parts":[[2022,4,21]],"date-time":"2022-04-21T01:55:51Z","timestamp":1650506151000},"page":"188","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Quadratic Equation in Split Quaternions"],"prefix":"10.3390","volume":"11","author":[{"given":"Wensheng","family":"Cao","sequence":"first","affiliation":[{"name":"School of Mathematics and Computational Science, Wuyi University, Jiangmen 529020, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Cao, W., and Chang, Z. (2020). Moore\u2013Penrose inverse of split quaternion. Linear Multilinear Algebra, 1\u201317.","DOI":"10.1080\/03081087.2020.1769015"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/s00006-014-0475-z","article-title":"Split-quaternions and the Dirac equation","volume":"25","author":"Antonuccio","year":"2015","journal-title":"Adv. Appl. Clifford Algebras"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Cao, W., and Tang, Z. (2021). Some similarities classes related to O(2,1) in split quaternion. Linear Multilinear Algebra, 1\u201322.","DOI":"10.1080\/03081087.2021.1873231"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"678","DOI":"10.1016\/j.aim.2011.06.001","article-title":"Split quaternionic analysis and separation of the series for SL(2,R) and SL(2,C)\/SL(2,R)","volume":"228","author":"Frenkel","year":"2011","journal-title":"Adv. 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Lett."},{"key":"ref_15","first-page":"3460257","article-title":"Some fixed points results of quadratic functions in split quaternions","volume":"2106","author":"Kwun","year":"2016","journal-title":"J. Funct. Spaces"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Munir, M., Nizami, A., Rasoo1, A., Saleem, M.S., and Kang, S.M. (2018). Fixed points results in algebras of split quaternion and octonion. 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