MathDB

1

Part of 2020 LIMIT Category 1

Problems(2)

LIMIT 2020 P1

Source: LIMIT 2020

4/11/2020
Find all polynomial P(x)P(x) with degree ≤n\leq nand non negative coefficients such that P(x)P(1x)≤P(1)2P(x)P(\frac{1}{x})\leq P(1)^2 for all positive xx. Here nn is a natuaral number
algebrapolynomial
Easy rationality

Source: LIMIT 2020 Cat 1 Obj P1

5/2/2020
If aa is a rational number and bb is an irrational number such that abab is rational, then which of the following is false?
(A)ab2ab^2 is irrational (B)a2ba^2b is rational (C)ab\sqrt{ab} is rational (D)a+ba+b is irrational
irrationallimit