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Answer by cknoll for Show that this sum of polynomials has no zeros with...
A former professor of me suggested the following argumentation:First, we rewrite the polynomial$$\begin{align}S(x) & = \prod_{j=1}^n (x + \lambda_{j}) +\sum_{i=1}^n k_i \cdot \prod_{j=1, j\neq i}^n...
View ArticleShow that this sum of polynomials has no zeros with positive real part
Let $0 < \lambda_1 \leq \ldots \leq \lambda_n $ and $k_1, \ldots, k_n> 0$.Let further $$\begin{align}P(x)&:=\prod_{i=1}^n (x+\lambda_i) = (x+\lambda_1)\cdot \ldots \cdot (x+\lambda_n)...
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