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