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Find the value of n

Source: 1964 AHSME Problem 7

September 12, 2012
AMC

Problem Statement

Let nn be the number of real values of pp for which the roots of x2−px+p=0 x^2-px+p=0 are equal. Then nn equals:
<spanclass=′latex−bold′>(A)</span> 0<spanclass=′latex−bold′>(B)</span> 1<spanclass=′latex−bold′>(C)</span> 2<spanclass=′latex−bold′>(D)</span> a finite number greater than 2<spanclass=′latex−bold′>(E)</span> an infinitely large number{{ <span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ 2 \qquad<span class='latex-bold'>(D)</span>\ \text{a finite number greater than 2} }\qquad<span class='latex-bold'>(E)</span>\ \text{an infinitely large number} }
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