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Carl Friedrich Gauss

In: A History of Algebra

Author

Listed:
  • Bartel Leenert van der Waerden

    (Universität Zürich, Mathematisches Institut)

Abstract

The most important contributions of Gauss to the theory of algebraic equations are: first, the complete solution of the “cyclotomic equation” (1) $$ {x^m} - 1 = 0 $$ by means of radicals, second, the proof that every polynomial in one variable with real coefficients is a product of linear and quadratic factors. This theorem implies what we now call the “fundamental theorem of algebra”: Every polynomial f(x) with complex coefficients is a product of linear factors.

Suggested Citation

  • Bartel Leenert van der Waerden, 1985. "Carl Friedrich Gauss," Springer Books, in: A History of Algebra, chapter 0, pages 89-102, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-51599-6_5
    DOI: 10.1007/978-3-642-51599-6_5
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