Problema 15

Notăm cu $\alpha$ partea reală a unei rădăcini din $\mathbb{C}\setminus\mathbb{R}$ a polinomului $f=X^3-X^2-X-1$. Atunci:

a) $\alpha\in\left(\dfrac{1}{2},1\right)$; b) $\alpha\in\left(\dfrac{1}{9},\dfrac{1}{4}\right)$; c) $\alpha\in(-2,-1)$; d) $\alpha\in\left(-1,-\dfrac{1}{2}\right)$; e) $\alpha\in\left(0,\dfrac{1}{2}\right)$; f) $\alpha\in\left(-\dfrac{1}{2},0\right)$.