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

Algebra Level 3

A function \(f: \mathbb{R} \rightarrow \mathbb{R}\) satisfies \( f (5-x) = f(5+x) \). If \(f(x) = 0 \) has \(5\) 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 \( x^*\) such that \( f(x^*) =0\).

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