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3 Distinct Integer Roots

Source: 2023 AMC 12B #14

November 15, 2023
algebrapolynomialAMCAMC 122023 AMC 12B2023 AMC

Problem Statement

For how many ordered pairs (a,b)(a,b) of integers does the polynomial x3+ax2+bx+6x^3+ax^2+bx+6 have 33 distinct integer roots?
<spanclass=′latex−bold′>(A)</span> 5<spanclass=′latex−bold′>(B)</span> 6<spanclass=′latex−bold′>(C)</span> 8<spanclass=′latex−bold′>(D)</span> 7<spanclass=′latex−bold′>(E)</span> 4<span class='latex-bold'>(A)</span>\ 5 \qquad<span class='latex-bold'>(B)</span>\ 6 \qquad<span class='latex-bold'>(C)</span>\ 8 \qquad<span class='latex-bold'>(D)</span>\ 7 \qquad<span class='latex-bold'>(E)</span>\ 4
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