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

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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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