Re: help with polynomial solutions

• To: mathgroup at smc.vnet.net
• Subject: [mg81780] Re: help with polynomial solutions
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Wed, 3 Oct 2007 02:36:08 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <fdt3dv\$rqj\$1@smc.vnet.net>

```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.

You must tell Mathematica that the identity a x^2 + b x + c == x^2 holds
for all x. Therefor, use *Reduce* and *ForAll* as in

In[1]:= Reduce[ForAll[x, a x^2 + b x + c == x^2], {a, b, c}]

Out[1]= a == 1 && b == 0 && c == 0

Regards,
--
Jean-Marc

```

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