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P7 IMC 2017

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Misalkan $p(x)$ adalah polinomial non-konstan dengan koefisien real. Untuk setiap bilangan asli $n$, misalkan $q_n(x)=(x+1)^np(x)+x^np(x+1)$. Buktikan kalau hanya ada hingga buah $n$ sehingga semua akar dari $q_n(x)$ adalah bilangan real.

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