MathDB

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Part of 2018 Moscow Mathematical Olympiad

Problems(3)

Trinomial and derivative

Source: Moscow Olympiad 2018, Grade 11, P1

4/7/2018
The graphs of a square trinomial and its derivative divide the coordinate plane into four parts. How many roots does this square trinomial has?
calculusderivativealgebra
Square of number

Source: Moscow Olympiad 2018, Grade 10, P1

7/13/2018
Is there a number in the decimal notation of the square which has a sequence of digits "20182018"?
number theory
Easy algebra

Source: Moscow Olympiad 2018, Grade 9, P1

7/13/2018
a1,a2,...,a81a_1,a_2,...,a_{81} are nonzero, ai+ai+1>0a_i+a_{i+1}>0 for i=1,...,80i=1,...,80 and a1+a2+...+a81<0a_1+a_2+...+a_{81}<0. What is sign of a1∗a2∗...∗a81a_1*a_2*...*a_{81}?
algebrainequalities