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NMTC 2023 FINALS P3 JUNIOR

Source: NMTC 2023 Finals P3 (Junior)

November 5, 2023
algebrapolynomialnmtc

Problem Statement

Let ai(i=1,2,3,4,5,6)a_i (i=1,2,3,4,5,6) are reals. The polynomial f(x)=a1+a2x+a3x2+a4x3+a5x4+a6a5+7x6−4x7+x8f(x)=a_1+a_2x+a_3x^2+a_4x^3+a_5x^4+a_6a^5+7x^6-4x^7+x^8 can be factorized into linear factors x−xix-x_i where i∈1,2,3,...,8i \in {1,2,3,...,8}. Find the possible values of a1a_1.
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