Algebraic solution

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The solution of an algebraic equation, often one that seeks zeros of a polynomial, is sometimes said to admit an "algebraic solution" or a "solution in radicals" if function that expresses the solution in terms of the coefficients relies only on addition, subtraction, multiplication, division, and the extraction of roots. The most well-known example is the solution

introduced in secondary school, of the quadratic equation

(where a ≠ 0).

The Abel-Ruffini theorem states that the general quintic equation lacks an algebraic solution.

An algebraic solution is not the same thing as a closed-form expression.