Question 15
Let $f(x)$ be a degree $2006$ polynomial with complex roots $c_{1}, c_{2}, \ldots, c_{2006}$, such that the set
$$
\left\{\left|c_{1}\right|,\left|c_{2}\right|, \ldots,\left|c_{2006}\right|\right\}
$$
consists of exactly $1006$ distinct values. What is the minimum number of real roots of $f(x)$?
$$
\left\{\left|c_{1}\right|,\left|c_{2}\right|, \ldots,\left|c_{2006}\right|\right\}
$$
consists of exactly $1006$ distinct values. What is the minimum number of real roots of $f(x)$?