2.38 For all real numbers $k$ less than 9, the equation
$$
(k-5) x^{2}-2(k-3) x+k=0
$$
(A) has no real roots.
(B) has only one real root.
(C) has two equal real roots.
(D) has two distinct real roots.
(E) the number of real roots cannot be determined.
(China Jilin Province Seven Cities and Prefectures Junior High School Mathematics Competition, 1985)
[Solution] When $k=5$, the equation becomes a first-degree equation, and naturally, at this time $k \neq 3$, the equation has a unique real root;
Also, when $k \neq 5$, consider
$$
\Delta=[-2(k-3)]^{2}-4 k(k-5)=36-4 k \text{. }
$$

Notice that $k0$, so the equation has two real roots.
In summary, the equation can have one or two real roots, hence the answer is $(E)$.