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Same here. Given Abel's Impossibility theorem [1], the headline got me very curious. Not that you couldn't solve for any case (the theorem talks about a general
by abhgh 8y ago
Same here. Given Abel's Impossibility theorem [1], the headline got me very curious. Not that you couldn't solve for any case (the theorem talks about a general solution), but still interesting.
[1] http://mathworld.wolfram.com/AbelsImpossibilityTheorem.html http://mathworld.wolfram.com/AbelsImpossibilityTheorem.html
- fspeech 8y agoSolving particular equations are definitely possible. Abel's theorem says there is no general formula to solve the quintic and higher order polynomials.
- abhgh 8y agoYeah, I realized that this would be potentially be confusing about what I meant, so I edited my comment.
- octachron 8y agoAbel-Ruffini theorem only speaks about general solution in term of elementary operations and nth-root, which is a very restricted form of solution. Numerically solving roots for generic polynomial is perfectly doable (and the nth-root already require approximate computation). Moreover, the radical solution for cubic and quartic equation is already quite difficult and inefficient to use compared to numerical solution.