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Condition for Real Solutions

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June 13, 2009

Problem Statement

For what real values of k k, other than k \equal{} 0, does the equation x^2 \plus{} kx \plus{} k^2 \equal{} 0 have real roots? <spanclass=′latex−bold′>(A)</span> k<0<spanclass=′latex−bold′>(B)</span> k>0<spanclass=′latex−bold′>(C)</span> k≥1<spanclass=′latex−bold′>(D)</span> all values of k<spanclass=′latex−bold′>(E)</span> no values of k <span class='latex-bold'>(A)</span>\ {k < 0}\qquad <span class='latex-bold'>(B)</span>\ {k > 0} \qquad <span class='latex-bold'>(C)</span>\ {k \ge 1} \qquad <span class='latex-bold'>(D)</span>\ \text{all values of }{k}\qquad <span class='latex-bold'>(E)</span>\ \text{no values of }{k}
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