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Epilogue

In: Quintic Equations and How to Solve Them

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  • C. M. Linton

Abstract

Our journey is over and we have reached our destination. Via a circuitous route, taking in complex numbers, fields, group theory and Galois theory, we have discovered that the generality and simplicity of the quadratic formula is the exception, not the rule. The formulas involved in solving cubic and quartic equations are hardly simple, but they are general. But that generality evaporates when we reach quintics, lost into the ether. Nevertheless, some quintic equations can be solved using only a finite number of the algebraic operations + , − , × , ÷ $$+,-,\times ,\div $$ and Square root symbol. and we have seen how to identify which quintics are solvable in this sense and shown how to solve them.

Suggested Citation

  • C. M. Linton, 2025. "Epilogue," Springer Books, in: Quintic Equations and How to Solve Them, chapter 10, pages 183-202, Springer.
    • Handle: RePEc:spr:sprchp:978-3-032-01658-4_10
    DOI: 10.1007/978-3-032-01658-4_10
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