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Almost quadratic equation has 100 roots

Source: 42nd International Tournament of Towns, Senior O-Level P4, Spring 2021

February 18, 2023
algebrarootsTournament of Towns

Problem Statement

It is well-known that a quadratic equation has no more than 2 roots. Is it possible for the equation ⌊x2⌋+px+q=0\lfloor x^2\rfloor+px+q=0 with p≠0p\neq 0 to have more than 100 roots?
Alexey Tolpygo
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