1. Given two quadratic trinomials $f(x)$ and $g(x)$ with leading coefficients of 1, each having two real roots, and $f(1)=g(2)$, $g(1)=f(2)$. Find the sum of the four roots of these two quadratic trinomials.
1.6.
$$
\text { Let } f(x)=x^{2}+a x+b, g(x)=x^{2}+c x+d \text {. }
$$

According to the conditions in the problem, we have
$$
\begin{array}{l}
1+a+b=4+2 c+d, \\
4+2 a+b=1+c+d .
\end{array}
$$
(1) - (2) gives
$$
-3-a=3+c \Rightarrow-a-c=6 \text {. }
$$

According to Vieta's formulas, $-a$ is the sum of the roots of the equation $f(x)=0$, and $-c$ is the sum of the roots of the equation $g(x)=0$. Therefore, the sum of the four roots of these two quadratic trinomials is 6.