Polynomial Equation and Inequality

Algebra Level 5

Let \(p(x), g(x), h(x)\) be a polynomial function such that \(\lambda\) is one of the real roots of \(p(x)=0\). If \(p(x) = (g(x) + h(x))^2 + c\) where \( c \geq 0\). Find the sum of maximum value and minimum value of \(c\).

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