12. In the complex plane, the two points $M, N$ correspond to the non-zero complex numbers $\alpha, \beta$ (O is the origin). If $2 \alpha^{2}-2 \alpha \beta+\beta^{2}=0$, then $\triangle O M N$ is a $\qquad$ triangle.
12. Isosceles right triangle. Since $2\left(\frac{\alpha}{\beta}\right)^{2}-2\left(\frac{\alpha}{\beta}\right)+1=0, \frac{\alpha}{\beta}=\frac{2 \pm \sqrt{-4}}{4}=\frac{1 \pm \mathrm{i}}{2}$, thus $a, \beta$ form an angle of $\frac{\pi}{4}$, and $\frac{|\alpha|}{|\beta|}=\frac{\sqrt{2}}{2}$, so the required triangle is an isosceles right triangle.