Let \( P(x) \) be a polynomial with real coefficients. Let \( a, b \in R \), \( ab \) be the two...

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Let \( P(x) \) be a polynomial with real coefficients. Let \( a, b \in R \), \( ab \) be the two consecutive roots of \( P(x) \). Prove that there exist \( c \) such that \( acb \) and \( P^{\prime}(c)+100 P(c)=0 \).
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