12. Given the quadratic equation with integer coefficients $t^{2}+x t+y=0$ has real roots $\alpha, \beta$, and $\alpha^{2}+\beta^{2}<4$, find the values of $x, y$.
12. By Vieta's formulas, we know $\alpha^{2}+\beta^{2}=(\alpha+\beta)^{2}-2 \alpha \beta=x^{2}-2 y\frac{x^{2}}{2}-2$. Also, $\Delta \geqslant 0$, which gives $y \leqslant \frac{x^{2}}{4}$. Using the graph of the quadratic function, the integer points within the shaded region are $(-2,1),(-1,-1),(-1,0),(0$, $-1),(0,0),(1,0),(1,-1),(2,1)$.