关键词: 一元三次方程, 有理根定理, 物理问题, 生成式人工智能

Abstract: This article illustrates the application of cubic equations in solving problems related to kinematics, dynamics, gravitational fields, electrostatic fields, and electromagnetic fields through five presented examples. These examples include mock exam questions from various provinces and cities as well as real exam questions from the college entrance examination. Using techniques such as rational root theorem and reasonable approximation, examples are given of how cubic equations can be factorized. Finally, the characteristics of high school physics problems involving cubic equations in analysis and solution are discussed, and examples are provided for reference on how to combine generative artificial intelligence software to empower test question design and teaching expansion. 

Key words: cubic equation, logical root theorem, physical issues, generative AI