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At most N^2 pairs has common root

Source: Saint Petersburg olympiad 2024, 10.4

September 22, 2024
algebra

Problem Statement

Let's consider all possible quadratic trinomials of the form x2+ax+bx^2 + ax + b, where aa and bb are positive integers not exceeding some positive integer NN. Prove that the number of pairs of such trinomials having a common root does not exceed N2N^2.
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