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Roots

Source: AMC 10 2006B, Problem 14

February 17, 2006
AMC

Problem Statement

Let a a and b b be the roots of the equation x^2 \minus{} mx \plus{} 2 \equal{} 0. Suppose that a \plus{} (1/b) and b \plus{} (1/a) are the roots of the equation x^2 \minus{} px \plus{} q \equal{} 0. What is q q? <spanclass=′latex−bold′>(A)</span>52<spanclass=′latex−bold′>(B)</span>72<spanclass=′latex−bold′>(C)</span>4<spanclass=′latex−bold′>(D)</span>92<spanclass=′latex−bold′>(E)</span>8 <span class='latex-bold'>(A) </span> \frac 52 \qquad <span class='latex-bold'>(B) </span> \frac 72 \qquad <span class='latex-bold'>(C) </span> 4 \qquad <span class='latex-bold'>(D) </span> \frac 92 \qquad <span class='latex-bold'>(E) </span> 8
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