# 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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