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Determine whether there exist real numbers a, b, c,t - ISL71

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September 22, 2010
algebraequationrootspolynomialIMO Shortlist

Problem Statement

Determine whether there exist distinct real numbers a,b,c,ta, b, c, t for which:
(i) the equation ax2+btx+c=0ax^2 + btx + c = 0 has two distinct real roots x1,x2,x_1, x_2,
(ii) the equation bx2+ctx+a=0bx^2 + ctx + a = 0 has two distinct real roots x2,x3,x_2, x_3,
(iii) the equation cx2+atx+b=0cx^2 + atx + b = 0 has two distinct real roots x3,x1.x_3, x_1.
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