Solving 4th Order Polynomials: Methods and Tips for Finding Roots

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    Polynomials
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Discussion Overview

The discussion revolves around methods for finding the roots of a 4th degree polynomial, particularly in the context of control engineering. Participants explore various approaches, including numerical methods and potential algebraic techniques.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant inquires about methods to find roots of a specific 4th degree polynomial and questions whether it can be factored into quadratics.
  • Another participant corrects the terminology from "order" to "degree" and mentions that while a solution exists, it is lengthy and suggests using software like Maple or Matlab for practical purposes.
  • A different participant notes that there is a formula for 4th degree polynomials similar to the quadratic formula, but emphasizes its complexity and recommends numerical approximation instead.
  • The original poster acknowledges the terminology mistake and expresses concern about the complexity of the solution, indicating they prefer to work it out by hand despite having used Matlab.
  • A repeated inquiry about methods for finding roots reinforces the original question and includes a link to a root-finding website.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best method for finding roots, with some advocating for numerical methods while others mention the existence of a complex algebraic solution. The discussion remains unresolved regarding the most effective approach.

Contextual Notes

Participants express uncertainty about the feasibility of factoring the polynomial and the practicality of using the lengthy algebraic formula. There is also a reliance on software tools, which may limit the exploration of manual methods.

rlspin
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Hey everyone

Im doing control engineering and was wondering what methods i could use to find the roots of a 4th order polynomial?

For example:

(x^4) + (8x^3) + (7x^2) + 6x = 5

Could I separate that into two brackets of quadratics or will i need to use a really long winded method?

Thanks in advance for any help
 
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'order'? You mean 'degree'! Well yes there is a solution for it but it is indeed long winded. You can try to find easy solutions by try. Else use Maple or Matlab.
 
A formula exists for 4 degree polynomials analogously to the quadratic formula, but it is very long and complicated and coding it into a program would take too much time. Just numerically approximate all the roots.
 
Sorry, i do mean degree! Slipped up cos I am working with a 4th order system.
I was worried id have to do it the long way.
I did use Matlab but wanted to see if I could work out the answer by hand.
Anywat, thanks for the help guys. I really appreciate it!
 
rlspin said:
Hey everyone

Im doing control engineering and was wondering what methods i could use to find the roots of a 4th order polynomial?

For example:

(x^4) + (8x^3) + (7x^2) + 6x = 5

Could I separate that into two brackets of quadratics or will i need to use a really long winded method?

Thanks in advance for any help
also check this website

http://xrjunque.nom.es/precis/rootfinder.aspx
 

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