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The quadratic formula, discovered independently by many ancient scholars, is a familiar sight to anyone who has studied mathematics. Less well known are formulas for the solutions of cubic and quartic equations whose discoveries were among the high points of sixteenth-century mathematics. Their study forms the heart of this book, as part of the broader theme that a polynomial's coefficients can be used to obtain detailed information on its roots. A closing chapter offers glimpses into the theory of higher-degree polynomials, concluding with a proof of the fundamental theorem of algebra. The book is designed for self-study, with exercises and historical notes provided throughout. It is ideal for high school students eager to go beyond the standard curriculum, undergraduates who desire an in-depth look at a topic they may have unwittingly skipped over, or teachers looking for ways to enhance their presentation of this fascinating topic.