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Re: Factor and/or Rules replacements

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  • Subject: [mg104486] Re: Factor and/or Rules replacements
  • From: Bill Rowe <readnews at>
  • Date: Sun, 1 Nov 2009 17:54:56 -0500 (EST)

On 11/1/09 at 3:56 AM, yves.dauphin at (yves) wrote:

>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?

>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?

after getting the solution you could do as follows:

In[8]:= sol/.HoldPattern[{{_ -> a_},{_ -> b_}}]->(x-a)(x-b)

Out[8]= ((1/2)(b-Sqrt[b^2 - 4*c])+x)((1/2)(Sqrt[b^2 - 4*c]+b)+x)

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