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Polynomial Algebra

Source: Iranian 3rd-Round MO 2019 ; mid-term Algabra Exam P3

July 31, 2019
algebrapolynomial

Problem Statement

We are given a natural number dd. Find all open intervals of maximum length I⊆RI \subseteq R such that for all real numbers a0,a1,...,a2d−1a_0,a_1,...,a_{2d-1} inside interval II, we have that the polynomial P(x)=x2d+a2d−1x2d−1+...+a1x+a0P(x)=x^{2d}+a_{2d-1}x^{2d-1}+...+a_1x+a_0 has no real roots.
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