Quadratika

Algebra Level 3

Let \(P_1(x\)) \(=\) \(x^2\) \(+\) \(a_1x\) \(+\) \(b_1\) and \(P_2(x)\) \(=\) \(x^2\) \(+\) \(a_2x\) \(+\) \(b_2\) be two quadratic polynomials with integer coefficients. Suppose \(a_1\) and \(a_2\) are distinct and there exist distinct integers \(m\) and \(n\) such that \(P_1(m)\) \(=\) \(P_2(n)\) and also \(P_2(m)\) \(=\) \(P_1(n)\). We can conclude that \(a_1\) \(-\) \(a_2\) is always :

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