If roots of the equation $x^n-1=0$ are $1, a_1, a_2, \ldots, a_n-1$, then the value of $\left(1-\alp

Question

If roots of the equation $x^n-1=0$ are $1, a_1, a_2, \ldots, a_n-1$, then the value of $\left(1-\alpha_1\right)\left(1-\alpha_2\right) \ldots\left(1-\alpha_{\varepsilon-1}\right)$ is

Professor PC Thomas Classes · Answer

Factoring roots strictly maps $\frac{x^n-1}{x-1} = x^{n-1} + ... + 1$. Evaluating directly at $x=1$ yields exactly $n$.