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# Thread Subject: Roots of 4th order polynomial

 Subject: Roots of 4th order polynomial From: Markus Buehren Date: 6 Nov, 2007 13:59:16 Message: 1 of 3 Hi! There is an analytical way to compute the roots of a polynomial of 4th degree, found by some guy called Ferrari. Here are two descriptions: http://mathworld.wolfram.com/QuarticEquation.html http://www.mathe.tu-freiberg.de/~hebisch/cafe/viertergrad.pdf (in german) I wonder why I can't find an implementation in Matlab (or C) of this algorithm on Matlab central. Does anyone know where to find one? Regards Markus
 Subject: Roots of 4th order polynomial From: l_combee@yahoo.no Date: 6 Nov, 2007 16:39:03 Message: 2 of 3 On Nov 6, 2:59 pm, "Markus Buehren" wrote: > Hi! > > There is an analytical way to compute the roots of a > polynomial of 4th degree, found by some guy called Ferrari. > Here are two descriptions: > > http://mathworld.wolfram.com/QuarticEquation.html > > http://www.mathe.tu-freiberg.de/~hebisch/cafe/viertergrad.pdf > (in german) There is a "simpler" (?) solution then the ones described above (the final results are obviously the same), and it doesn't require one to "eliminate" the x^3 term. Just rewrite as follows: x^4 + a1*x^3 + a2*x^2 + a3*x + a4 => (x^2 + b1*x + b3)*(x^2 + b2*x + b4) b1,2,3,4 are simple linear and intuitive expressions in a1,2,3,4 with an additional unknown parameter r, e.g., b1 = a1/2 + r b2 = a1/2 - r b3/2 = a2 - 1/4*a1^2 + r^2 - (...)/r b4/2 = a2 - 1/4*a1^2 + r^2 + (...)/r where r is a non-zero root of the cubic equation r^3 + k*r^2 + l*r^2 + m = 0 and where k,l,m are again simple expressions of the a1,2,3,4 Voila.
 Subject: Roots of 4th order polynomial From: Markus Buehren Date: 8 Nov, 2007 00:40:43 Message: 3 of 3 > There is a "simpler" (?) solution then the ones described above (the > final results are obviously the same), and it doesn't > require one to "eliminate" the x^3 term. > > Just rewrite as follows: Do you have an implementation of that method?? Markus