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Wednesday, February 10, 2010

Polynomial and Complex Number

Let $\alpha$ be a root of polynomial
$$P(x)=x^n+a_{n-1}x^{n-1}+\cdots+a_1 x+a_0$$
where $a_i \in [0,1]$, for $i=1,2,\dots,n-1$. Prove that
$$Re(\alpha)<\frac{1+\sqrt{5}}{2}.$$

Proposed by Bogdan Enescu,Romania

1 comment:

  1. iki soal tahap 2 pas jamanku tho?

    kok ra ono soal combin?

    ReplyDelete