# There's only one way

Calculus Level 4

$$f(x)$$ is a $$6^\text{th}$$ degree polynomial satisfying $$f(1-x)=f(x+1)$$ for all real values of $$x$$. If $$f(x)$$ has four distinct real roots and two real and equal roots, then find the sum of all roots of $$f(x)=0$$.

×