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Re: Factor and/or Rules replacements

  • To: mathgroup at smc.vnet.net
  • Subject: [mg104500] Re: [mg104443] Factor and/or Rules replacements
  • From: "David Park" <djmpark at comcast.net>
  • Date: Sun, 1 Nov 2009 17:57:34 -0500 (EST)
  • References: <24397765.1257066820598.JavaMail.root@n11>

f[b_, c_] = Function[x, x^2 + b x + c]

(x - Root[f[b, c], 1]) (x - Root[f[b, c], 2])


David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/  


From: yves [mailto:yves.dauphin at solvay.com] 


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?

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?

With anticipated thanks.
Yves




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