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### Abstract

This entry formalises two well-known results about the geometric relation between the *roots*
of a complex polynomial and its *critical points*, i.e. the roots of its derivative.

The first of these is the *GauÃŸâ€“Lucas Theorem*: The critical points of a
complex polynomial lie inside the convex hull of its roots.

The second one is *Jensen's Theorem*: Every non-real critical point of a
real polynomial lies inside a disc between two conjugate roots. These discs are called the *Jensen discs*: the Jensen disc of a pair of conjugate roots $a \pm b i$ is the smallest disc that contains both of them, i.e. the disc with centre $a$ and
radius $b$.