What did Galois determine for polynomials?
A rule for ordinary differentiation
A necessary and sufficient condition for solvability by radicals
A theory for complex numbers
A method for integral calculations
Answer
Galois' determination for polynomials states that a polynomial is solvable by radicals if and only if its Galois group is solvable. Solvable groups are those that can be built up from alternating and symmetric groups through extensions. This criterion provides a definitive way to classify polynomials based on their solvability properties.
Gallant Galois: The Life and Legacy of a French Mathematician
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