Abstract
Because polynomial functions are completely determined by their roots, every property of a polynomial is affected when these roots change. Our research aims to further our understanding of how the distribution of a polynomial's roots affects specjfic characteristics of the function. We are especially interested in classifying which root distributions maximize or minimize certain properties. We employ recent results on polynomial root dragging and root motion to explore these issues further, including the attempt to explain why many properties are maximized by Bernstein polynomials. This paper will survey some important results and present our investigations into new problems and approaches.
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