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Putnam 1957 A4

Session A

$P(z)$ is a complex polynomial whose roots (as points in the Argand plane) can be covered by a closed circular disc of radius $R$ . Show that the roots of $n P(z)-k P^{\prime}(z)$ can be covered by a closed circular disc of radius $R$ $+|k|$ , where $n$ is the degree of $P(z), k$ is any complex number, and $P^{\prime}(z)$ is the derivative of $P(z)$ .

Dataset text PutnamGAP. Quoted with source.

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