Let's determine $k$ such that the expression

$$
(5-k) x^{2}-2(1-k) x+2-2 k
$$

is negative for all values of $x$.

The given expression is negative for all values of $x$ if it has a maximum and if this maximum value is negative. If $5-k>0$, then the expression has a maximum. The maximum value is

$$
\frac{2(5-k)(1-k)-(1-k)^{2}}{5-k}=\frac{(k-1)(k-9)}{5-k}
$$

Since $5-k>0 \quad \text { or if } \quad k-9>0
$$

which implies

$$
k>9
$$

(Jánosy Gyula, Budapest.)

The problem was also solved by: Bánó L., Csada I., Dömény I., Epstein K., Fodor H., Földes R., Haar A., Heimlich P., Messer P., Schuster Gy., Schwarz O., Sonnenfeld J.