Let $\alpha \neq 1$ be a real root of the equation $x^3-ax^2+ax-1=0,$ where $a \neq -1$ is a real number. Then a root of this equation, among the following, is :

$\begin {array} {1 1} (1)\;\alpha^2 & \quad (2)\;-\frac{1}{\alpha} \\ (3)\;\frac{1}{\alpha} & \quad (4)\;-\frac{1}{\alpha^2} \end {array}$

$(3)\;\frac{1}{\alpha}$
answered Nov 7, 2013 by