In layman terms, why is it not possible to algebraically solve polynomials of degree five and higher?
2026-04-04 16:15:12.1775319312
Algebraic solution of high degree polynomials
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One author phrased it thusly (more or less): In a polynomial, every root is an irrational function of the coefficients, but every coefficient is only a rational function of the roots. This dichotomy sets up a sort of 'internal tension' between the roots and the coefficients, which increases with the degree of the polynomial. By degree 5 the 'tension' has exceeded the representational capacity of nested root-extractions.