Kvant Math Problem 1569

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Verdicts: FAIL + FAIL
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Problem

Construct a polynomial with rational coefficients whose minimum value is

  1. $-\sqrt{2}$,
  2. $\sqrt{2}$.
  3. Prove that a quartic polynomial satisfying the conditions of part b) does not exist.
  4. Do there exist polynomials with integer coefficients satisfying conditions a) and b)?

A. V. Spivak

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