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Coefficients b and c

Source: AHSME 1963 Problem 24

January 10, 2014
quadraticsAMC

Problem Statement

Consider equations of the form x2+bx+c=0x^2 + bx + c = 0. How many such equations have real roots and have coefficients bb and cc selected from the set of integers {1,2,3,4,5,6}\{1,2,3, 4, 5,6\}?
<spanclass=latexbold>(A)</span> 20<spanclass=latexbold>(B)</span> 19<spanclass=latexbold>(C)</span> 18<spanclass=latexbold>(D)</span> 17<spanclass=latexbold>(E)</span> 16<span class='latex-bold'>(A)</span>\ 20 \qquad <span class='latex-bold'>(B)</span>\ 19 \qquad <span class='latex-bold'>(C)</span>\ 18 \qquad <span class='latex-bold'>(D)</span>\ 17 \qquad <span class='latex-bold'>(E)</span>\ 16