1. The equation $(k-1) x^{2}+3 k x+(2 k+3)=0$ has roots greater than -5 and less than $-\frac{3}{2}$. Then the range of values for $k$ is
II. $1 . k=1$ or $\frac{11}{6}0$.
Let $f(x)=(k-1) x^{2}+3 k x+(2 k+3)$.
When $k>1$, $k-1>0$,
By the necessary and sufficient conditions for the distribution of roots of a quadratic equation
$$
\begin{array}{l}
f(-5)>0 \Rightarrow k>\frac{11}{6}, \\
f\left(-\frac{3}{2}\right)>0 \Rightarrow k<3 . \\
\text { Hence } \frac{11}{6}<k<3 .
\end{array}
$$

When $k<1$, $k-1<0$,
$$
f(-5)<0 \text { , } f\left(-\frac{3}{2}\right)<0 \Rightarrow \text { no solution. }
$$

Note: This problem can also express the two roots when $k \neq 1$ and establish the inequality relationship with $-5, -\frac{3}{2}$. Similarly, solve for the range of $k$.