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P5 IMC 2017

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Misalkan $k,n$ bilangan asli dimana $n\ge k^2-3k+4$, dan misalkan $f(z)=z^{n-1}+c_{n-2}z^{n-2}+...+c_0$ adalah sebuah polinomial dengan koefisien kompleks sehingga $c_0c_{n-2}=c_1c_{n-3}=...=c_{n-2}c_0=0$. Buktikan bahwa $f(z)$ dan $z^n-1$ punya maksimal $n-k$ akar yang sama.

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