# 4th order polynomials

1. Nov 28, 2010

### rlspin

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

Thanks in advance for any help

2. Nov 28, 2010

### Outlined

'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. Nov 28, 2010

### Gib Z

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. Nov 28, 2010

### rlspin

Sorry, i do mean degree! Slipped up cos im 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. Jan 30, 2012

### abypatel

also check this website

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