roots of polynomials
 

How can I obtain roots of fourth order plynomail without using numerical algorithms. pratap

Re: roots of polynomials
 

Make a search typing "Ludovico Ferrari". He developped a method for finding roots of fourth degree polynomials

Re: roots of polynomials
 

Do you have any particular refernces. pratap

Re: roots of polynomials
 

I have one, it explains all the method of Ludovico Ferrari, but it's in french !!

Here is the link : http://www.epre.ch/math/ferrari_M.pdf

Hope this helps

Re: roots of polynomials
 

Go look in the CRC Handbook for the solution to a quartic polynomial. If you have access to Mathematica, type

ans = Solve[a*x^4 + b*x^3 + c*x^2 + d*x + e==0,x];

x1 = Factor[Part[x /. ans, 1]];

x2 = Factor[Part[x /. ans, 2]];

x3 = Factor[Part[x /. ans, 3]];

x4 = Factor[Part[x /. ans, 4]];

It's a huge mess.

How about these:

http://mathworld.wolfram.com/QuarticEquation.html

http://www.sosmath.com/algebra/factor/fac12/fac12.html

Re: roots of polynomials
 

Sorry guys I need to find the roots of polynomial of fifth order. Can you help me now pratap

Re: roots of polynomials
 

http://library.wolfram.com/examples/quintic/main.html

Use Mathematica and use NSolve.

Re: roots of polynomials
 

There is no general formula for the roots of a quintic and so you'll need to do it numerically. If you know one or more of the roots you can factorize and then use one of the formulas for a lower order polynomial.

Re: roots of polynomials
 

I have an old book Numerical Methods in Fortran by John M. McCormick and Mario G. Salvadori Prentice Hall, 1964 which gives an algorithm and a Fortran II code for exact roots of a quartic equation. The authors call it Brown's method but do not provide any reference. Although the book is old and one may consider it to be outdated, but it's still a useful book. The programs are really very well written. (You will enjoy seeing PUNCH statement!) For a 5th order polynomial, it shouldn't be difficult to write a code: One root may be found by, say, Newton-Raphson method, and the remaining by the method of the above book. Regards.

Re: roots of polynomials
 

I have a Fortran 95 code that uses the bisection method to find roots of any polynomial. If you have a compiler I will send to code to you by email. If you dont hav a complier I can give you the website to get a free compiler. If you want to post the polynomial I can run it for you and give you the roots.