"Unlike quadratic, cubic, and quartic polynomials, the general quintic cannot be solved algebraically"

math is just trolling us.

A friend suggests this may be due to the ending up with multiple solutions in one quadrant. which kinda makes sense to me, a person who doesn't know how math works

Mathematicians are too cowardly to ever answer the "why" question huh


@cinebox it's nothing to do with quadrants! In a nutshell, if you study the types of numbers you can construct with +-*/ and nth roots, there's a connection to a certain mathematical "group". If you can solve a polynomial with +-*/ and nth roots, that translates to a certain group being "solvable", meaning having some smaller groups inside it. Then you can prove there are some groups which 1. Some quintic polynomials can be translated into, and 2. Aren't solvable.

The name of the type of math which the proof is using is "Galois theory".

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