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

In summary, the conversation discusses finding the roots of a 4th order polynomial in control engineering. It is mentioned that there is a formula for it, but it is complicated and time-consuming to code into a program. The use of Maple or Matlab is suggested for finding easy solutions, or numerically approximating the roots. A helpful website is also mentioned for finding roots.
  • #1
rlspin
6
0
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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  • #2
'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.
 
  • #3
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.
 
  • #4
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!
 
  • #5
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
 

1. What is a 4th order polynomial?

A 4th order polynomial is a mathematical expression with a degree of 4, meaning it contains terms that are raised to the power of 4. It can be written in the form ax^4 + bx^3 + cx^2 + dx + e, where a, b, c, d, and e are constants.

2. How many solutions does a 4th order polynomial have?

A 4th order polynomial can have up to four solutions, depending on the values of the coefficients and whether or not they are real or complex numbers.

3. What are the properties of a 4th order polynomial?

A 4th order polynomial has the following properties: it has four terms, its graph has at most four turning points, its end behavior is determined by the leading coefficient, and its degree is 4.

4. How do you solve a 4th order polynomial?

To solve a 4th order polynomial, you can use the following methods: factoring, synthetic division, graphing, or by using the quartic formula.

5. What are some real-life applications of 4th order polynomials?

Some real-life applications of 4th order polynomials include modeling population growth, predicting the trajectory of a projectile, and designing curved structures in architecture.

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