$2 \cdot 20$ The sum of two numbers is 6, and the absolute value of their difference is 8. The quadratic equation with these two numbers as roots is
(A) $x^{2}-6 x+7=0$.
(B) $x^{2}-6 x-7=0$.
(C) $x^{2}+6 x-8=0$.
(D) $x^{2}-6 x+8=0$.
(E) $x^{2}+6 x-7=0$.
(6th American High School Mathematics Examination, 1955)
[Solution] Let the two numbers be $\alpha, \beta$, then from the problem we have
$$
\left\{\begin{array}{l}
\alpha+\beta=6, \\
|\alpha-\beta|=8 .
\end{array}\right.
$$
$(1)^{2}-(2)^{2}$ gives $4 \alpha \beta=-28$, i.e., $\alpha \beta=-7$.
$\therefore \alpha, \beta$ are the two roots of the equation $x^{2}-6 x-7=0$. Therefore, the answer is $(B)$.