MathDB

16

Part of 2001 National Olympiad First Round

Problems(1)

P16 [Algebra] - Turkish NMO 1st Round - 2001

Source:

4/20/2014
The polynomial P(x)=x3+ax+1P(x)=x^3+ax+1 has exactly one solution on the interval [−2,0)[-2,0) and has exactly one solution on the interval (0,1](0,1] where aa is a real number. Which of the followings cannot be equal to P(2)P(2)?
<spanclass=′latex−bold′>(A)</span> 17<spanclass=′latex−bold′>(B)</span> 303<spanclass=′latex−bold′>(C)</span> 26−1<spanclass=′latex−bold′>(D)</span> 30<spanclass=′latex−bold′>(E)</span> 103 <span class='latex-bold'>(A)</span>\ \sqrt{17} \qquad<span class='latex-bold'>(B)</span>\ \sqrt[3]{30} \qquad<span class='latex-bold'>(C)</span>\ \sqrt{26}-1 \qquad<span class='latex-bold'>(D)</span>\ \sqrt {30} \qquad<span class='latex-bold'>(E)</span>\ \sqrt [3]{10}
algebrapolynomial