A simple functional equation

Algebra Level 4

Let f(x) f(x) be a function that satisfies

f(2014+x)=f(2014x).f(2014 + x) = f(2014 - x) .

If f f has exactly 3 3 roots being α,β,γ \alpha, \beta, \gamma , what is the value of α+β+γ? \alpha + \beta + \gamma ?

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