Let P(x)=(x−x1)(x−x2)...(x−xn) where all the n roots are real and distinct. Let y1,y2,...,yn−1 be the roots of P′. Show that
min.
My thoughts: We have P'(x) = P(x)(\frac1{x-x_1}+...+\frac1{x-x_n}). So we may consider P'(x)/P(x), which has poles at the roots of P.
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