$$P(x)=x^n+a_{n-1}x^{n-1}+\cdots+a_1 x+a_0$$
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
Solat Idul Fitri di ‘s-Hertogenbosch
3 years ago
Showing posts with label Polynomial. Show all posts
Showing posts with label Polynomial. Show all posts
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
$$Re(\alpha)<\frac{1+\sqrt{5}}{2}.$$
$$P(x)=x^n+a_{n-1}x^{n-1}+\cdots+a_1 x+a_0$$
where $a_i \in [0,1]$, for $i=1,2,\dots,n-1$. Prove that
$$Re(\alpha)<\frac{1+\sqrt{5}}{2}.$$
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