$4 \cdot 25$ The equation $7 x^{2}-(k+13) x+k^{2}-k-2=0$ (where $k$ is a real number) has two real roots $\alpha, \beta$, and $0<\alpha<1, \quad 1<\beta<2$. The range of values for $k$ is
(A) $3<k<4$.
(B) $-2<k<-1$.
(C) $3<k<4$ or $-2<k<-1$.
(D) No solution.
(China Junior High School Mathematics League, 1990)
[Solution] Let $f(x)=7 x^{2}-(k+13) x+k^{2}-k-2$, as shown in the figure, we have
$$
\left\{\begin{array}{l}
f(0)=k^{2}-k-2>0, \\
f(1)=k^{2}-2 k-80 .
\end{array}\right.
$$

Solving this, we get $3<k<4$ or $-2<k<-1$.
Therefore, the answer is $(C)$.