Beyond the quadratic formula [electronic resource] / Ron Irving.
- Other records:
- Washington, D.C. : Mathematical Association of America, 2013.
- Classroom resource materials (Unnumbered)
Classroom resource materials
1 online resource (0 p.)
- Electronic books.
- The quadratic formula for the solution of quadratic equations was discovered independently by scholars in many ancient cultures and is familiar to everyone. Less well known are formulas for solutions of cubic and quartic equations whose discovery was the high point of 16th century mathematics. Their study forms the heart of this book, as part of the broader theme that a polynomials 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 also includes historical sections designed to reveal key discoveries in the study of polynomial equations as milestones in intellectual history across cultures. Beyond the Quadratic Formula is designed for self-study, with many results presented as exercises and some supplemented by outlines for solution. The intended audience includes in-service and prospective secondary mathematics teachers, 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, and the mathematically curious who wish to do some work to unlock the mysteries of this beautiful subject.
- front cover ; copyright page ; title page ; Preface; Contents; Polynomials; Definitions; Multiplication and Degree; Factorization and Roots; Bounding the Number of Roots; Real Numbers and the Intermediate Value Theorem; Graphs; Quadratic Polynomials; Sums and Products; Completing the Square; Changing Variables; A Discriminant; History; Cubic Polynomials; Reduced Cubics; Cardano's Formula; Graphs; A Discriminant; History; Complex Numbers; Complex Numbers; Quadratic Polynomials and the Discriminant; Square and Cube Roots; The Complex Plane; A Geometric Interpretation of Multiplication
Euler's and de Moivre's FormulasRoots of Unity; Converting Root Extraction to Division; History; Cubic Polynomials, II; Cardano's formula; The Resolvent; The Discriminant; Cardano's Formula Refined; The Irreducible Case; Viète's Formula; The Signs of the Real Roots; History; Quartic Polynomials; Reduced Quartics; Ferrari's Method; Descartes' Method; Euler's Formula; The Discriminant; The Nature of the Roots; Cubic and Quartic Reprise; History; Higher-Degree Polynomials; Quintic Polynomials; The Fundamental Theorem of Algebra; Polynomial Factorization; Symmetric Polynomials
A Proof of the Fundamental TheoremReferences; Index; About the Author
- Description based upon print version of record.
Includes bibliographical references and index.
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