Iterated Quadratic Roots

★ 8/10complex numbers algebra Polynomials Casework Vieta's Formulas

Problem

Let $P(x)$ be a monic quadratic with complex coefficients. The equation $P(P(x)) = 0$ has four distinct solutions $x = 3, 4, a, b$ . Find the sum of all possible values of $(a+b)^2$ .

Answer

Solution

Difficulty	8/10
Topics	complex numbers, algebra, Polynomials, Casework, Vieta's Formulas

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