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Roots of equation

Source: 1959 AHSME Problem 44

August 14, 2013
LaTeXalgebrapolynomialVietaAMC

Problem Statement

The roots of x2+bx+c=0x^2+bx+c=0 are both real and greater than 11. Let s=b+c+1s=b+c+1. Then s:s: <spanclass=′latex−bold′>(A)</span> may be less than zero<spanclass=′latex−bold′>(B)</span> may be equal to zero <span class='latex-bold'>(A)</span>\ \text{may be less than zero}\qquad<span class='latex-bold'>(B)</span>\ \text{may be equal to zero}\qquad <spanclass=′latex−bold′>(C)</span> must be greater than zero<spanclass=′latex−bold′>(D)</span> must be less than zero<span class='latex-bold'>(C)</span>\ \text{must be greater than zero}\qquad<span class='latex-bold'>(D)</span>\ \text{must be less than zero}\qquad <spanclass=′latex−bold′>(E)</span> must be between -1 and +1<span class='latex-bold'>(E)</span>\text{ must be between -1 and +1}
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