MathNet 2016-part-07 — 182 problems (EN–VI) Question 161

Let $q(x) = q^{1}(x) = 2x^{2} + 2x - 1$, and let $q^{n}(x) = q(q^{n-1}(x))$ for $n \gt 1$. How many negative real roots does $q^{2016}(x)$ have?