Solution
= Solution
In <characteristic of a field>[characteristic] two, the <formal derivative in positive characteristic> of
$$
f(T)=T^3+aT+b
$$
is
$$
f'(T)=T^2+a.
$$
A <polynomial> is separable exactly when it and its derivative have no common root. If $r$ is a root of $f'$, then
$$
f(r)=r^3+ar+b=r(r^2+a)+b=b.
$$
\b[Thus $f$ and $f'$ have a common root exactly when $b=0$. Therefore $f$ is a <separable polynomial> if and only if $b\ne0$.]