       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 is 2 and not -2.

Andrzej Kozlowski

```

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