Re: NSolve unable to find all possible roots

*To*: mathgroup at smc.vnet.net*Subject*: [mg115595] Re: NSolve unable to find all possible roots*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Sun, 16 Jan 2011 05:50:55 -0500 (EST)

On 15 Jan 2011, at 10:45, Luiz Melo wrote: > Dear mathgroup, > The equation below has three possible roots, namely: 0., 1.99, -1.99. > > eq = x*(Sqrt[-13.319 - x^2] + 2.41*Sqrt[1.004 - x^2]) > > If we try NSolve[eq == 0, x], we get {{kx-> 0.}} only. > > How to instruct NSolve to search for the other two roots of the above equation? > > Thank you > Luiz Melo > You have some unconventional ideas about the meaning of "root" in mathematics. For example, 1.99 is not normally regarded as a "root" since: eq = x*(Sqrt[-13.319 - x^2] + 2.41*Sqrt[1.004 - x^2]); N[eq /. x -> 1.99] 0. + 16.51780004580277*I which is not-zero. However, if you wish to regard what is known as "parasite solutions" as roots, you can get them too: Solve[eq == 0, x, VerifySolutions -> False] // N {{x->-1.99573},{x->0.},{x->1.99573}} You should be aware that most people will not regard your "solutions" as correct just as it is the usual convention that Sqrt[4] is 2 and not -2. Andrzej Kozlowski