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Turkish NMO First Round - 2012 Problem - 15 {Algebra}

Source:

July 1, 2012

Problem Statement

If x4+8x3+18x2+8x+a=0x^4+8x^3+18x^2+8x+a = 0 has four distinct real roots, then the real set of aa is
<spanclass=latexbold>(A)</span> (9,2)<spanclass=latexbold>(B)</span> (9,0)<spanclass=latexbold>(C)</span> [9,0)<spanclass=latexbold>(D)</span> [8,1)<spanclass=latexbold>(E)</span> (8,1) <span class='latex-bold'>(A)</span>\ (-9,2) \qquad <span class='latex-bold'>(B)</span>\ (-9,0) \qquad <span class='latex-bold'>(C)</span>\ [-9,0) \qquad <span class='latex-bold'>(D)</span>\ [-8,1) \qquad <span class='latex-bold'>(E)</span>\ (-8,1)