## Task B-1.1.

Determine all integers $x$ for which the expression $x^{4}-101 x^{2}+100$ has a negative value.
## Solution.

We solve the inequality $x^{4}-101 x^{2}+100<0$ in the set of integers.

We factorize the left side of the inequality:

$$
\begin{array}{cc}
x^{4}-101 x^{2}+100<0 & \\
x^{4}-100 x^{2}-x^{2}+100<0 & \\
x^{2}\left(x^{2}-100\right)-\left(x^{2}-100\right)<0 & \\
\left(x^{2}-1\right)\left(x^{2}-100\right)<0 & 2 \text { points } \\
(x-1)(x+1)(x-10)(x+10)<0 . & 1 \text { point }
\end{array}
$$

Using the sign table, we can obtain the solution in the set $\mathbb{R}:\langle-10,-1\rangle \cup\langle 1,10\rangle$. 2 points The integers from the obtained intervals are $\{-9,-8,-7,-6,-5,-4,-3,-2,2,3,4,5,6,7,8,9\}$.