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Find k for quadratic

Source: AHSME 1963 Problem 28

January 11, 2014
quadraticsAMC

Problem Statement

Given the equation 3x2−4x+k=03x^2 - 4x + k = 0 with real roots. The value of kk for which the product of the roots of the equation is a maximum is:
<spanclass=′latex−bold′>(A)</span> 169<spanclass=′latex−bold′>(B)</span> 163<spanclass=′latex−bold′>(C)</span> 49<spanclass=′latex−bold′>(D)</span> 43<spanclass=′latex−bold′>(E)</span> −43<span class='latex-bold'>(A)</span>\ \dfrac{16}{9} \qquad <span class='latex-bold'>(B)</span>\ \dfrac{16}{3}\qquad <span class='latex-bold'>(C)</span>\ \dfrac{4}{9} \qquad <span class='latex-bold'>(D)</span>\ \dfrac{4}{3} \qquad <span class='latex-bold'>(E)</span>\ -\dfrac{4}{3}
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