Quadratic Coefficients Inequality

Algebra Level 5

Suppose \(p(x) = ax^2 + bx + c\) is a quadratic polynomial with real coefficients and \( |p(x)| \le 1 \) for all values of \(x\) in the range \( [0,1] \). Find the largest possible value of \( |a| + |b| + |c| \).

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