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The function $f(x)$ has exactly six different roots, and is such that $f(11+x)=f(11-x)$. How do you find the sum of the roots ?

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up vote 6 down vote accepted

The condition implies that if $r$ is a root so is its reflection with respect to $11$. Thus the six roots can be organized into three pairs, each summing 22, and the sum of all six roots is 66.

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