Find the number of real solutions of tan²(x) - 8 tan(x) + 14 = 0 in [0, 2π].
Correct: A
Solve quadratic in tan(x): tan(x) = [8 ± √(64 - 56)]/2 = [8 ± √8]/2 = 4 ± √2. Two solutions for tan(x) each valid twice in [0, 2π], but check if any lead to invalid values. Since tan(x) is defined except at π/2 + nπ, and 4 ± √2 are finite, total solutions = 2 values * 2 quadrants each = 4 solutions.