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Solving non-linear equations plays a fundamental role in mathematics. Often, such tasks are formulated as root-finding problems. Determining the roots of linear or quadratic polynomials is the simplest example and is already known from school. In particular, closed formulas, such as the quadratic formula, can be given here. However, for polynomials of degree five and higher, there are no such closed formulas for the solutions.

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Root Finding Problems

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  • 发表日期：

    2026年

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  • Thomas Richter,
  • Henry von Wahl,
  • Thomas Wick

摘要

Solving non-linear equations plays a fundamental role in mathematics. Often, such tasks are formulated as root-finding problems. Determining the roots of linear or quadratic polynomials is the simplest example and is already known from school. In particular, closed formulas, such as the quadratic formula, can be given here. However, for polynomials of degree five and higher, there are no such closed formulas for the solutions.