The three roots of the equation f(x) = 0 are x = -2, 0, and 3. What are the three values of x for which f(x - 3) = 0? A. -5, -3, 0 B. -2, 0, 3 C. 0, 6, 9 D. 1, 3, 6

GATE 2018 · General Aptitude · Polynomials · easy

Answer: The three values are x = 1, 3, 6 (option D).

1. Identify what f(x - 3) = 0 requires: f(x - 3) = 0 means the argument (x - 3) must belong to the set of roots of f, which is {-2, 0, 3}. So we need x - 3 = -2, or x - 3 = 0, or x - 3 = 3.
2. Solve each sub-equation for x: Case 1: x - 3 = -2 => x = 1. Case 2: x - 3 = 0 => x = 3. Case 3: x - 3 = 3 => x = 6. The three values are x = 1, 3, 6.