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# Let be the ordered pairs of real numbers such that the polynomial has exactly one distinct real root and no nonreal complex roots. Find .

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Let \( (a_1,b_1), (a_2,b_2), \dots,(a_n,b_n)\) be the ordered pairs \((a,b)\) of real numbers such that the polynomial \(p(x) = (x^2 + ax + b)^2 +a(x^2 + ax + b) - b\)
has exactly one distinct real root and no nonreal complex roots. Find \(a_1 + b_1 + a_2 + b_2 + \dots + a_n + b_n \).

May 12, 2022