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Turkey NMO 2007 1st Round - P03 (Algebra)

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October 4, 2012

Problem Statement

Let a<b<c<da<b<c<d be integers. If one of the roots of the equation (x−a)(x−b)(x−c)(x−d)−9(x-a)(x-b)(x-c)(x-d)-9 is x=7x=7, what is a+b+c+da+b+c+d?
<spanclass=′latex−bold′>(A)</span> 14<spanclass=′latex−bold′>(B)</span> 21<spanclass=′latex−bold′>(C)</span> 28<spanclass=′latex−bold′>(D)</span> 42<spanclass=′latex−bold′>(E)</span> 63 <span class='latex-bold'>(A)</span>\ 14 \qquad<span class='latex-bold'>(B)</span>\ 21 \qquad<span class='latex-bold'>(C)</span>\ 28 \qquad<span class='latex-bold'>(D)</span>\ 42 \qquad<span class='latex-bold'>(E)</span>\ 63
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