Solve the following equation:

$$
x^{4}+2 x^{3}-x^{2}-2=0
$$
The equation has two real roots: $x_{1}=1, \quad x_{2} \approx-2.56$. $x_{2}$ is irrational, and to determine it, an approximate method must be used. From the fourth graders, we expected an explanation of why there are exactly two real roots.