There is no general algebraic formula, using only the four arithmetic operations and radicals, for the roots of a polynomial equation of degree five or higher. Proved by Niels Henrik Abel, building on earlier work of Paolo Ruffini, it closed a centuries-old search for a general quintic formula.
Facts
StatementThere is no solution in radicals to general polynomial equations of degree five or higher, with coefficients treated as indeterminates. 1 Connections
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1. Abel-Ruffini Theorem (Wikipedia)
Wikimedia Foundationlead paragraph, first sentence
the Abel-Ruffini theorem (also known as Abel's impossibility theorem) states that there is no solution in radicals to general polynomial equations of degree five or higher with arbitrary coefficients
lead paragraph, attribution sentence
The theorem is named after Paolo Ruffini, who made an incomplete proof in 1799 (which was refined and completed in 1813 and accepted by Cauchy), and Niels Henrik Abel, who provided a proof in 1824.
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