2013-23 Polynomials with rational zeros

Find all polynomials \( P(x) = a_n x^n + \cdots + a_1 x + a_0 \) satisfying (i) \( a_n \neq 0 \), (ii) \( (a_0, a_1, \cdots, a_n) \) is a permutation of \( (0, 1, \cdots, n) \), and (iii) all zeros of \( P(x) \) are rational.

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7 thoughts on “2013-23 Polynomials with rational zeros

  1. 학생

    {a0, … , an}과 {0, … , n}이 일대일 대응이고, P(x)=0의 해가 모두 유리수인 다항식 p(x)를 모두 찾는 것이 맞는지 여쭈어도 될까요?^^;;

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