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P11 [Algebra] - Turkish NMO 1st Round - 2014

Source:

May 22, 2014
quadratics

Problem Statement

What is the product of real numbers aa which make x2+ax+1x^2+ax+1 a negative integer for only one real number xx?
<spanclass=latexbold>(A)</span> 1<spanclass=latexbold>(B)</span> 2<spanclass=latexbold>(C)</span> 4<spanclass=latexbold>(D)</span> 6<spanclass=latexbold>(E)</span> 8 <span class='latex-bold'>(A)</span>\ -1 \qquad<span class='latex-bold'>(B)</span>\ -2 \qquad<span class='latex-bold'>(C)</span>\ -4 \qquad<span class='latex-bold'>(D)</span>\ -6 \qquad<span class='latex-bold'>(E)</span>\ -8