Anyone know how to solve a quintic or quartic?

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Discussion Overview

The discussion centers around methods for solving quintic and quartic polynomials, exploring both theoretical and practical approaches. Participants share insights on the existence of formulas and techniques applicable to these types of polynomials.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • Some participants note that there is no general formula equivalent to the quadratic formula for quintic polynomials, while a formula exists for quartic polynomials, though its practical use may be limited.
  • One participant suggests using the remainder theorem as a potential method for solving these polynomials, but acknowledges that its effectiveness can vary depending on the specific case.
  • Another participant raises a question about the specific goals of the original poster, asking for clarification on whether they are looking to solve a general polynomial.
  • There is mention of using polynomial coefficients to derive results, but this approach is also noted to depend on the context of the application.

Areas of Agreement / Disagreement

Participants generally agree that while quartic polynomials have a solvable formula, quintic polynomials do not have a straightforward equivalent. However, there is no consensus on the best method to approach solving these polynomials, as various techniques are proposed with differing levels of effectiveness.

Contextual Notes

Limitations include the lack of a universally applicable formula for quintic polynomials and the conditional nature of the proposed methods, which may depend on specific polynomial characteristics or applications.

Who May Find This Useful

This discussion may be of interest to students and practitioners in mathematics and engineering who are exploring polynomial equations, particularly those dealing with higher-degree polynomials.

13habelbrea
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Anyone know how to solve a quintic or quartic? (thanks)
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There is no equivalent to the quadratic formula for quintic polynomials if that's what you're getting at. There is for quartic polynomials, but it's not something you really want to use.

http://planetmath.org/encyclopedia/QuarticFormula.html

Can you explain a bit more what you want to do? Is it really just solve a general polynomial?
 
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The easiest way would be to use the remainder theorem, but that's hit/miss. A lot of times you can use the coefficients to get the result you're after, but that depends on the application.
 

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