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integer polynomial with min real root \sqrt2

Source: III Soros Olympiad 1996-97 R1 11.8 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

May 29, 2024
algebrapolynomial

Problem Statement

Find any polynomial with integer coefficients, the smallest value of which on the entire line is equal to :
a) −2-\sqrt2 b) 2\sqrt2
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