$\begin{array}{l}
a^{2} b^{2} x^{2}+b^{2} x-a^{2} x-1=0 \\
\Rightarrow b^{2} x\left(a^{2} x+1\right)-1\left(a^{2} x+1\right)=0 \\
\Rightarrow\left(b^{2} x-1\right)\left(a^{2} x+1\right)=0 \\
\Rightarrow\left(b^{2} x-1\right)=0 \text { or }\left(a^{2} x+1\right)=0 \\
\Rightarrow x=\frac{1}{b^{2}} \text { or } x=\frac{-1}{a^{2}}
\end{array}$

Hence, $\frac{1}{b^{2}}$ and $\frac{-1}{a^{2}}$ are the roots of the given equation.