Example 1. For the equation $(1984 x)^{2}-1983 \times 1985 x-1$ $=0$, the larger root is $r$, and for the equation $x^{2}+1983 x-1984=0$, the smaller root is $s$. What is $r-s$? (1984 Beijing Junior High School Mathematics Competition Question)
Solve $\because 1984^{2}+(-1983) \times 1985$ $+(-1)=0$, according to property 1, we can get the roots of the first equation $x_{1}=1, \quad x_{2}=-\frac{1}{1984^{2}}$.

Also $\because 1+1983-1984=0$, we can get the roots of the second equation $x_{1}^{\prime}=1, x_{2}^{\prime}=-1984$.
$$
\text { Therefore } r-s=1985 \text {. }
$$