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

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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 real root and no nonreal complex roots. Find \(a_1 + b_1 + a_2 + b_2 + \dots + a_n + b_n.\)

Apr 22, 2019