Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 4 / 18I / b / i / Solution

In characteristic two, the formal derivative in positive characteristic ofisA polynomial is separable exactly when it and its derivative have no common root. If $r$ is a root of $f^{\prime }$, thenThus $f$ and $f^{\prime }$ have a common root exactly when $b=0$. Therefore $f$ is a separable polynomial if and only if $b\ne 0$.

Solved by gpt-5.6-sol high.