The discussion focuses on determining the maximum magnitude of coefficients a, b, and c in the quadratic equation |ax² + bx + c| ≤ 1 for all x in the interval [0, 1]. The initial analysis reveals that setting x = 0 leads to |c| ≤ 1, establishing that the maximum magnitude of c is 1. Further exploration indicates that the coefficients a and b cannot be independently constrained; instead, their values are interdependent based on the behavior of the quadratic function within the defined bounds. The key insight is that the entire curve must remain within the box defined by x = 0, x = 1, y = -1, and y = 1.
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