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You can find more information and change your preferences here. Make interactive worksheets. Video tutorial. Get started. Make interactive workbooks. Teachers access. Then for a few hundred more years, mathematicians search for a formula to the quintic equation satisfying these same properties. Galois invented groups in order to solve this problem. Although, instead of finding a formula, he proved that no such formula exists for the quintic, or indeed for any higher degree polynomial.
When we say that no such formula exists, we mean there is no formula involving only the coefficients and the operations mentioned; there are other ways to find roots of higher degree polynomials. It should be noted that Niels Henrik Abel also proved that the quintic is unsolvable, and his solution appeared earlier than that of Galois, although Abel did not generalize his result to all higher degree polynomials.
It is clear, however, that Galois did not know of Abel's solution, and the idea of a group was revolutionary. Section 4.
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