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Using Coefficient on an equation

If f=a*x^2+b*x+c, Coefficient[f,x^2] obviously returns a.
But if f=a*x^2+b*x+c==0, it returns 0.

The problem arose using the Calculus`VariationalMethods` package.
It (unfortunately) returns the Euler-Lagrange equations as
such, so I have to remove the useless ==0 appendage for
Coefficient to work properly. Is there a simple direct way out?

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