4. When $x=\frac{1+\sqrt{1994}}{2}$, the value of the polynomial $\left(4 x^{3}-1997 x-\right.$ $1994)^{2001}$ is ( ).
(A) 1
(B) -1
(C) $2^{2001}$
(D) $-2^{200 \mathrm{i}}$
$$
\begin{array}{l}
\text{Since } x=\frac{1+v^{\prime} 1994}{2}, \text{ then } (2, r-1)^{2}=1994, \text{ i.e., } 4 x^{2}-4 x-1993=0. \text{ Thus,} \\
\left(4 x^{3}-1997 x-1994\right)^{2001}: \\
=\left(\left(4 x^{2}-4 x-1993\right) x+\left(4 x^{2}-4 x-1993\right)\right. \\
-1)^{2001} \\
=(-1)^{2001}=-1 .
\end{array}
$$