Question 6
When the roots of the polynomial
$$
\begin{gathered} P(x)=(x-1)^1(x-2)^2 \\ {}\cdot (x-3)^3\cdots \\ {}\cdot (x-10)^{10} \end{gathered}
$$
are removed from the number line, what remains is the union of $11$ disjoint open intervals. On how many of these intervals is $P(x)$ positive?
$$
\begin{gathered} P(x)=(x-1)^1(x-2)^2 \\ {}\cdot (x-3)^3\cdots \\ {}\cdot (x-10)^{10} \end{gathered}
$$
are removed from the number line, what remains is the union of $11$ disjoint open intervals. On how many of these intervals is $P(x)$ positive?