On factorization of quadratic polynomials with single parameter generalized quaternion coefficients
DENG Yong1,2
(1.College of Mathematics and Statistics， Kashi University， Kashi 844006， Xinjiang， China； 2.Research Center of Modern Mathematics and Its Application， Kashi 844006， Xinjiang， China)
Abstract：In this paper， the factorization problem of single parameter generalized quaternion coefficient quadratic polynomials in the form of P(t)＝t2＋bt＋c is studied under different conditions. Based on whether the coefficients of quadratic polynomials have correlation， we divide them into two categories： coefficient linearly correlated and coefficient linearly independent. We provide sufficient and necessary conditions for the factorization of these two types of quadratic polynomials. Moreover， the relevant factorization formula for quadratic polynomials that can be factorized is obtained.
邓 勇,. 关于单参数广义四元数系数二次多项式的因式分解[J]. 华中师范大学学报(自然科学版), 2025, 59(1): 105-110.
DENG Yong,. On factorization of quadratic polynomials with single parameter generalized quaternion coefficients. journal1, 2025, 59(1): 105-110.
2025, Vol. 59 
