Re: Viewing real solution out of Root[#] output

• To: mathgroup at smc.vnet.net
• Subject: [mg50656] Re: [mg50645] Viewing real solution out of Root[#] output
• From: Andrzej Kozlowski <andrzej at akikoz.net>
• Date: Wed, 15 Sep 2004 07:54:26 -0400 (EDT)
• References: <200409150550.BAA11775@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```The function Root takes two parameters and as you have only one I am
not sure if I understand your correctly. It is used to represent roots
of polynomial equations but itself is not an equation and it does not
have "solutions". However, the following may be relevant.

If the polynomial equation equation

f[x]==0

has real roots than they are "counted" (by the second parameter of
Root) before the imaginary ones. So if your equation has a real root
then Root[f[#]&,1] will be real. E.g.

f[x_] = x^3 - x^2 + 4*x - 4;

Root[f[#1] & , 1]

1

Now consider a polynomial with two real roots:

g[x_] = (x - 3)*f[x];

then

(Root[g[#1] & , #1] & ) /@ Range[4]

{1, 3, -2*I, 2*I}

As you see the roots

Root[#1^4 - 4*#1^3 + 7*#1^2 - 16*#1 + 12, 1]

1

and

Root[#1^4 - 4*#1^3 + 7*#1^2 - 16*#1 + 12, 2]

3

are both real.

Andrzej Kozlowski
Chiba, Japan
http://www.akikoz.net/~andrzej/
http://www.mimuw.edu.pl/~akoz/

On 15 Sep 2004, at 14:50, Mukhtar wrote:

> *This message was transferred with a trial version of CommuniGate(tm)
> Pro*
> Is there a way to view the real solution (no matter how many pages it
> would take just to print it) for output of the form something like
> Root[x#1+2x#1-3#2] and so on, where x is some symbolic parameter?
>
>

```

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