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\[ P\left( x\right) =\left|\begin{array}[c]{cccc}1 & 1 &\ldots & 1\\ a_{1}& a_{2}&\ldots & x\\ a_{1}^{2}& a_{2}^{2}&\ldots & x^{2}\\ \vdots & & &\\ a_{1}^{n-1}& a_{2}^{n-1}&\ldots & x^{n-1}\end{array}\right| . \]

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