MathDB

3

Part of 2017 Azerbaijan EGMO TST

Problems(2)

Day 1 Problem 3

Source: 2016 Russian Regional Olympiad

2/20/2017
In △\bigtriangleupABCABC BLBL is bisector. Arbitrary point MM on segment CLCL is chosen. Tangent to ⊙\odot(ABC)(ABC) at BB intersects CACA at PP. Tangents to ⊙\odotBLMBLM at BB and MM intersect at point QQ. Prove that PQPQ∥\parallelBLBL.
geometry
Real roots of the equation P(P(x))=0

Source: Azerbaijan EGMO TST 2017, D2 P3

7/31/2023
The degree of the polynomial P(x)P(x) is 2017.2017. Prove that the number of distinct real roots of the equation P(P(x))=0P(P(x)) = 0 is not less than the number of distinct real roots of the equation P(x)=0.P(x) = 0.
algebraPolynomialsReal Roots