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Problem 20 - Entrance Test

If (x² - 5x + 6) is a factor of x⁴ - 9x³ + 26x² - 24x, find the sum of all real roots of the quartic.

Correct: D

Factor: x(x³ - 9x² + 26x - 24). Given factor x² - 5x + 6 = (x-2)(x-3). Divide cubic by this to get (x-4) remaining. Roots 0,2,3,4. Sum = 9.