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Solve x^2-3x+c=0

Source: 1976 AHSME Problem 6

May 15, 2014
AMC

Problem Statement

If cc is a real number and the negative of one of the solutions of x2−3x+c=0x^2-3x+c=0 is a solution of x2+3x−c=0x^2+3x-c=0, then the solutions of x2−3x+c=0x^2-3x+c=0 are
<spanclass=′latex−bold′>(A)</span>1, 2<spanclass=′latex−bold′>(B)</span>−1, −2<spanclass=′latex−bold′>(C)</span>0, 3<spanclass=′latex−bold′>(D)</span>0, −3<spanclass=′latex−bold′>(E)</span>32, 32<span class='latex-bold'>(A) </span>1,~2\qquad<span class='latex-bold'>(B) </span>-1,~-2\qquad<span class='latex-bold'>(C) </span>0,~3\qquad<span class='latex-bold'>(D) </span>0,~-3\qquad <span class='latex-bold'>(E) </span>\frac{3}{2},~\frac{3}{2}
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