BALKAN-SL 2007 A2

Find all values of $a \in \mathbb{R}$ for which the polynomial \begin{align*} f(x)=x^4-2x^3 + \left(5-6a^2 \right)x^2 + \left(2a^2-4 \right)x + \left(a^2 -2 \right)^2 \end{align*} has exactly three real roots.