Question 12
When the roots of the polynomial $$
P(x) = (x-1)^1(x-2)^2(x-3)^3 \cdots (x-10)^{10}
$$ are removed from the real number line, what remains is the union of $11$ disjoint open intervals. On how many of those intervals is $P(x)$ positive?
P(x) = (x-1)^1(x-2)^2(x-3)^3 \cdots (x-10)^{10}
$$ are removed from the real number line, what remains is the union of $11$ disjoint open intervals. On how many of those intervals is $P(x)$ positive?