# 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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