IMO Shortlist 1971 problem 8


Kvaliteta:
  Avg: 0,0
Težina:
  Avg: 0,0
Dodao/la: arhiva
2. travnja 2012.
LaTeX PDF
Determine whether there exist distinct real numbers a, b, c, t for which:

(i) the equation ax^2 + btx + c = 0 has two distinct real roots x_1, x_2,

(ii) the equation bx^2 + ctx + a = 0 has two distinct real roots x_2, x_3,

(iii) the equation cx^2 + atx + b = 0 has two distinct real roots x_3, x_1.
Izvor: Međunarodna matematička olimpijada, shortlist 1971