MathDB
roots of two quadratic equation

Source: 0

April 28, 2009
quadratics

Problem Statement

a a is a real number. x1 x_1 and x2 x_2 are the distinct roots of x^2 \plus{} ax \plus{} 2 \equal{} x. x3 x_3 and x4 x_4 are the distinct roots of (x \minus{} a)^2 \plus{} a(x \minus{} a) \plus{} 2 \equal{} x. If x_3 \minus{} x_1 \equal{} 3(x_4 \minus{} x_2), then x_4 \minus{} x_2 will be ?
<spanclass=latexbold>(A)</span> a2<spanclass=latexbold>(B)</span> a3<spanclass=latexbold>(C)</span> 2a3<spanclass=latexbold>(D)</span> 3a2<spanclass=latexbold>(E)</span> None<span class='latex-bold'>(A)</span>\ \frac {a}{2} \qquad<span class='latex-bold'>(B)</span>\ \frac {a}{3} \qquad<span class='latex-bold'>(C)</span>\ \frac {2a}{3} \qquad<span class='latex-bold'>(D)</span>\ \frac {3a}{2} \qquad<span class='latex-bold'>(E)</span>\ \text{None}