       Re: Factor and/or Rules replacements

• To: mathgroup at smc.vnet.net
• Subject: [mg104499] Re: [mg104443] Factor and/or Rules replacements
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sun, 1 Nov 2009 17:57:22 -0500 (EST)

```f = 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)

f // Expand

b*x + c + x^2

Bob Hanlon

---- yves <yves.dauphin at solvay.com> 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?

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[] /. x -> x1), (sol[] /. 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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