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Re: help with polynomial solutions

• To: mathgroup at smc.vnet.net
• Subject: [mg81779] Re: [mg81704] help with polynomial solutions
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Wed, 3 Oct 2007 02:35:37 -0400 (EDT)
• References: <200710020928.FAA28247@smc.vnet.net>

Several ways:

SolveAlways[a*x^2 + b*x + c == x^2, x]
{{a -> 1, b -> 0, c -> 0}}

LogicalExpand[a*x^2 + b*x + c == x^2 + O[x]^3]
1 - a == 0 && -b == 0 && -c == 0

or even

Solve[!Eliminate[a*x^2 + b*x + c != x^2, x]]
{{a -> 1, b -> 0, c -> 0}}

Andrzej Kozlowski


On 2 Oct 2007, at 18:28, Jules P. Aronson wrote:

> I could not get mathematica to solve the following class of problems.
>
> If f(x) and g(x) and two polynomials then a solution to force f(x)  
> to be
> equal to g(x) is the equate the coefficients of f(x) to be the same as
> those of g(x).  For example,
>
> a x^2 + b x + c  == x^2, has a solution, a=1, b=0, c=0.
>
> If I do the following in mathematica:
>
> Solve[a x^2 + b x + c == x^2, {a,b,c}] or using Reduce, I do not  
> get the
> desired solution.
>
> Can someone tell how to force mathematica to solve such problems.
>

• Follow-Ups:
  • Bug ???
    • From: Artur <grafix@csl.pl>

• References:
  • help with polynomial solutions
    • From: "Jules P. Aronson" <aronson@nlm.nih.gov>