Difference between revisions of "2023 AMC 10B Problems/Problem 12"

Revision as of 15:36, 15 November 2023

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?

@@ Line 1: / Line 1: @@
-Stop.
+When the roots of the polynomial
-Don't talk to me.
-Loser, lame-o, wannabe
+<math>P(x)  = (x-1)^1 (x-2)^2 (x-3)^3 \cdot \cdot \cdot (x-10)^{10}</math>
-Like oh, totally.
-T-t-totally.
+are removed from the number line, what remains is the union of 11 disjoint open intervals. On how many of these intervals is <math>P(x)</math> positive?
-Stop.
-Don't talk to me.
-Loser, lame-o, wannabe
-Like oh, totally.
-T-t-totally.