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 \(a_1 + b_1 + a_2 + b_2 + \dots + a_n + b_n \).

Guest May 12, 2022