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Integer-Zero Polynomial

Source: AMC 10 2010A Problem 21

February 10, 2010
algebrapolynomialVietaAMC

Problem Statement

The polynomial x^3\minus{}ax^2\plus{}bx\minus{}2010 has three positive integer zeros. What is the smallest possible value of a a? <spanclass=′latex−bold′>(A)</span> 78<spanclass=′latex−bold′>(B)</span> 88<spanclass=′latex−bold′>(C)</span> 98<spanclass=′latex−bold′>(D)</span> 108<spanclass=′latex−bold′>(E)</span> 118 <span class='latex-bold'>(A)</span>\ 78 \qquad <span class='latex-bold'>(B)</span>\ 88 \qquad <span class='latex-bold'>(C)</span>\ 98 \qquad <span class='latex-bold'>(D)</span>\ 108 \qquad <span class='latex-bold'>(E)</span>\ 118
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