← Back to Test

Problem 1 - Entrance Test

If the roots of x³ - 12x² + kx - 216 = 0 are in geometric progression, find k.

Correct: D

Let the roots be a/r, a, ar. Product = a³ = 216 → a = 6. Sum = 6(1/r + 1 + r) = 12 → r + 1/r = 1 → r² - r + 1 = 0 → r = 1 (double) is impossible, so use sum of products two at a time: 6·6(1/r + 1 + r) = k → 36·2 = 72.