Solving Q_1^2 - 111Q_1 + 2618 = 0: Q_1 = 47 or Q_1 = 58. Solving Q_2^2 - 121Q_2 + 3420 = 0: Q_2 = 57 or Q_2 = 60. If Q_1=47 and Q_2=57: Q_1 < Q_2. If Q_1=58 and Q_2=57: Q_1 > Q_2. Since different combinations give different relationships, the correct answer is E - relationship cannot be established.