Re: Why is the negative root?

*To*: mathgroup at smc.vnet.net*Subject*: [mg69479] Re: [mg69474] Why is the negative root?*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Thu, 14 Sep 2006 06:54:46 -0400 (EDT)*References*: <200609130803.EAA18412@smc.vnet.net>

On 13 Sep 2006, at 17:03, p-valko at tamu.edu wrote: > (Reduce[{z^3-z^2- b z-1==0, b>0, z>0}, z] //ToRadicals)/.b->3.//Chop > > gives a negativ z: > > z == - 0.414214 > > What am I doing wrong? > > Regards > Peter > Why do you need to use ToRadicals here? There is no point in it and, in fact you, are only asking for trouble. I am not sure why Mathematica even tries to convert Root objects with parameters to radicals, since it can't be done reliably due to branching problems and is of no practical use whatever, but at least the Help tells you that: â?¼ If Root objects in expr contain parameters, ToRadicals[expr] may yield a result that is not equal to expr for all values of the parameters. And, of course, if you do not use ToRadicals, there is no problem: Reduce[{z^3 - z^2 - b*z - 1 == 0, b > 0, z > 0}, z] /. b -> 3 z == 1 + Sqrt[2] Andrzej Kozlowski Tokyo, Japan

**References**:**Why is the negative root?***From:*p-valko@tamu.edu