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Roots of the Sum of Two Quadratics

Source: 2015 amc 10b #14

February 26, 2015
quadraticsAMC

Problem Statement

Let aa, bb, and cc be three distinct one-digit numbers. What is the maximum value of the sum of the roots of the equation (x−a)(x−b)+(x−b)(x−c)=0(x-a)(x-b)+(x-b)(x-c)=0? <spanclass=′latex−bold′>(A)</span>15<spanclass=′latex−bold′>(B)</span>15.5<spanclass=′latex−bold′>(C)</span>16<spanclass=′latex−bold′>(D)</span>16.5<spanclass=′latex−bold′>(E)</span>17<span class='latex-bold'>(A) </span> 15 \qquad<span class='latex-bold'>(B) </span> 15.5 \qquad<span class='latex-bold'>(C) </span> 16 \qquad<span class='latex-bold'>(D) </span> 16.5 \qquad<span class='latex-bold'>(E) </span> 17
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