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2023 AMC 10B Problems/Problem 12

Revision as of 15:36, 15 November 2023 by Andliu766 (talk | contribs)

When the roots of the polynomial

$P(x) = (x-1)^1 (x-2)^2 (x-3)^3 \cdot \cdot \cdot (x-10)^{10}$

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?

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