# 2. CONDITION

Find some function $f(x)$ for which the equations $f(x)=0$ and $f^{\prime}(x)+x^{2}+1=0$ have the same non-empty set of roots.
Solution. Indeed, the equations $-x=0$ and $(-x)'+x^{2}+1=0$ both have the unique root $\mathrm{x}=0$.

Answer. For example, $f(x)=-x$.