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This note presents a new proof of Gauss-Lucas theorem refinements, suggesting their complementary nature.
In this note, we give a new proof of a refinement of the Gauss-Lucas theorem given in [6]. The new proof uses a technique used to produce and older refinement of the same theorem in [3]. It was observed that the two refinements are complimentary to each other and we hope that this work explains why this is so.
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Hristo S. Sendov (2025) studied this question.
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