Let $$a,b$$ and $$c$$ be real numbers with $$a\ne 0$$. If $$\alpha$$ is a root of the equation $$a^2 x^2 + bx + c = 0$$, and $$\beta$$ is a root of $$a^2x^2-bx-c= 0$$ and $$0<\alpha <\beta$$, then the equation $$a^2 x^2 + 2bx + 2c = 0$$ has a root $$\gamma$$ that satisfies: