$\begin{array}{l}
\frac{2}{x^{2}}-\frac{5}{x}+2=0 \\
\Rightarrow 2-5 x+2 x^{2}=0 \\
\Rightarrow 2 x^{2}-5 x+2=0 \\
\Rightarrow 2 x^{2}-(4 x+x)+2=0 \\
\Rightarrow 2 x^{2}-4 x-x+2=0 \\
\Rightarrow 2 x(x-2)-1(x-2)=0 \\
\Rightarrow(2 x-1)(x-2)=0 \\
\Rightarrow 2 x-1=0 \text { or } x-2=0 \\
\Rightarrow x=\frac{1}{2} \text { or } x=2
\end{array}$

Hence, the roots of the equation are $\frac{1}{2}$ and 2 .