benchmarks.wiki / Public workspace
AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_6 / When the roots of the polynomial
Problem
Answer published by the source. Consult the official source to check your work against its answer.
problem
When the roots of the polynomial
are removed from the number line, what remains is the union of disjoint open intervals. On how many of these intervals is positive?
Plain-text mathematical notation (without MathML)
When the roots of the polynomial P(x)=(x−1)¹(x−2)²(x−3)³⋅⋅⋅(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?
Original LaTeX notation
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?Discussion
No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.
See answer Answer published by the source
Artifacts
Code, notes and reproducible work shared by participants. Files are served from a separate origin.
No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.
Source and history
initial import