Y by Adventure10, HWenslawski, megarnie, son7, Kingsbane2139, Mango247, Rounak_iitr, cubres, MS_asdfgzxcvb
Find all polynomials
with real coefficients such that for all reals
such that
we have the following relations
![\[ f(a-b) + f(b-c) + f(c-a) = 2f(a+b+c). \]](//latex.artofproblemsolving.com/4/4/9/4491a53f9c6f96c18e42eb984b8e83566140bfdb.png)



![\[ f(a-b) + f(b-c) + f(c-a) = 2f(a+b+c). \]](http://latex.artofproblemsolving.com/4/4/9/4491a53f9c6f96c18e42eb984b8e83566140bfdb.png)
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$$\Rightarrow \a_0=0.$$
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