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March 17, 2005, 04:54 |
roots of polynomials
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#1 |
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How can I obtain roots of fourth order plynomail without using numerical algorithms. pratap
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March 17, 2005, 05:12 |
Re: roots of polynomials
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#2 |
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Make a search typing "Ludovico Ferrari". He developped a method for finding roots of fourth degree polynomials
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March 17, 2005, 06:50 |
Re: roots of polynomials
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#3 |
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Do you have any particular refernces. pratap
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March 17, 2005, 08:04 |
Re: roots of polynomials
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#4 |
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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 |
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March 17, 2005, 16:41 |
Re: roots of polynomials
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#5 |
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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 |
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March 18, 2005, 02:25 |
Re: roots of polynomials
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#6 |
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Sorry guys I need to find the roots of polynomial of fifth order. Can you help me now pratap
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March 18, 2005, 02:52 |
Re: roots of polynomials
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#7 |
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March 18, 2005, 04:42 |
Re: roots of polynomials
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#8 |
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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.
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March 19, 2005, 21:31 |
Re: roots of polynomials
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#9 |
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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.
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March 19, 2005, 23:32 |
Re: roots of polynomials
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#10 |
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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.
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