Polynomial Roots with no complex roots 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 $a_1 + b_1 + a_2 + b_2 + \dots + a_n + b_n.$
I have no idea how to do this. Can someone help please?

Hint: a polynomial with exactly one root must be of the form $c (x - r)^n$ where $r$ is the root and $c$ is some nonzero constant. 
