Real Roots of f(5-x)=f(5+x)

Algebra Level 3

A function f:RRf: \mathbb{R} \rightarrow \mathbb{R} satisfies f(5x)=f(5+x) f (5-x) = f(5+x) . If f(x)=0f(x) = 0 has 55 distinct real roots, what is the sum of all of the distinct real roots?

Details and assumptions

The root of a function is a value x x^* such that f(x)=0 f(x^*) =0.

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