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Smaller Root of Equation

Source: 1964 AHSME Problem 8

September 12, 2012
AMC

Problem Statement

The smaller root of the equation (x−34)(x−34)+(x−34)(x−12)=0 \left(x-\frac{3}{4}\right)\left(x-\frac{3}{4}\right)+\left(x-\frac{3}{4}\right)\left(x-\frac{1}{2}\right) =0 is:
<spanclass=′latex−bold′>(A)</span> −34<spanclass=′latex−bold′>(B)</span> 12<spanclass=′latex−bold′>(C)</span> 58<spanclass=′latex−bold′>(D)</span> 34<spanclass=′latex−bold′>(E)</span> 1{{ <span class='latex-bold'>(A)</span>\ -\frac{3}{4}\qquad<span class='latex-bold'>(B)</span>\ \frac{1}{2}\qquad<span class='latex-bold'>(C)</span>\ \frac{5}{8}\qquad<span class='latex-bold'>(D)</span>\ \frac{3}{4} }\qquad<span class='latex-bold'>(E)</span>\ 1 }
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