If \( P(1)=0 \) and \( \frac{d P(x)}{d x}P(x), \forall x \geq 1 \),...

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If \( P(1)=0 \) and \( \frac{d P(x)}{d x}P(x), \forall x \geq 1 \), then prove that \( P(x)0, \forall x1 \).
(2003, 4M)
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