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

  • Thread starter Thread starter rlspin
  • Start date Start date
  • Tags Tags
    Polynomials
Click For Summary
To find the roots of a 4th degree polynomial, methods include numerical approximation and using software like Maple or Matlab. While there is a complex formula analogous to the quadratic formula for 4th degree polynomials, it is often impractical for manual calculations. Users can attempt to factor the polynomial into quadratics, but this may not always be feasible. Many recommend focusing on numerical methods for efficiency. Overall, for control engineering applications, leveraging computational tools is advisable.
rlspin
Messages
6
Reaction score
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
 
Physics news on Phys.org
'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
 
Thread 'How to define a vector field?'

Thread 'How to define a vector field?'

Hello! In one book I saw that function ##V## of 3 variables ##V_x, V_y, V_z## (vector field in 3D) can be decomposed in a Taylor series without higher-order terms (partial derivative of second power and higher) at point ##(0,0,0)## such way: I think so: higher-order terms can be neglected because partial derivative of second power and higher are equal to 0. Is this true? And how to define vector field correctly for this case? (In the book I found nothing and my attempt was wrong...
View full post »

Similar threads

Undergrad Looking for a creative or quick method for finding roots in GF(p^n)
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad What can be deduced about the roots of this polynomial?
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Why Use Nonlinear Polynomials for Linearization?
  • · Replies 10 ·
Replies
10
Views
4K
Undergrad Need help solving for X in third order polynomial
  • · Replies 15 ·
Replies
15
Views
3K
MHB Irreducible Polynomial g = X^4 + X + 1 over F2
  • · Replies 3 ·
Replies
3
Views
2K
MHB What Are the Roots and Generators of the Polynomial $g$ in $\mathbb{F}_{16}$?
  • · Replies 11 ·
Replies
11
Views
3K
MHB Eisenstein polynomial and field extension
  • · Replies 24 ·
Replies
24
Views
5K
Graduate Solution?: Quintic Equation from Physical System
  • · Replies 4 ·
Replies
4
Views
2K
High School What are the applications of roots of a polynomial?
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Question about the roots of Chebyshev polynomials
  • · Replies 2 ·
Replies
2
Views
2K