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Re: Factor and/or Rules replacements

  • To: mathgroup at smc.vnet.net
  • Subject: [mg104493] Re: [mg104443] Factor and/or Rules replacements
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sun, 1 Nov 2009 17:56:14 -0500 (EST)
  • References: <200911010856.DAA19674@smc.vnet.net>

On 1 Nov 2009, at 17:56, yves wrote:

> Hello everybody,
>
> Here is the model problem:
> I tried to obtain the factorisation of x^2+b x +c and expected to  
> get something like (x-1/2(-b+Sqrt[b^2-4 c))((x-1/2(-b-Sqrt[b^2-4 c)).
>
> So I tried
> in:Factor[x^2+b x + c] and get
> out: c + b x + x^2
> So my first question what should I have done?

Nothing. Factor factors only over the field of algebraic numbers, not  
algebraic functions.

>
> I tried another way
> in:sol=Solve[x^2+b x + c == 0,{x}]; and get the couple of  
> replacement rules.
> Next I defined
> in: f=(x-x1)(x-x2)
> and finally I replaced x1 and x2 in succession by
> in:f /. {(sol[[1]] /. x -> x1), (sol[[2]] /. x -> x2)}
> which gave the expected factorisation but enclosed in {}.
> My second question is :
> Is there a simpler way or more compact to replace x1 and x2?

You can do simply:

  Times @@ (x - (x /. Solve[x^2 + b x + c == 0, x]))

  (1/2 (b-Sqrt[b^2-4 c])+x) (1/2 (Sqrt[b^2-4 c]+b)+x)

Andrzej Kozlowski


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