How to tackle this polynomial given as a determinant? Let $$p (x) = \begin{vmatrix}
1 & x & x & \dots & x & x \\
x & 1 & x & \dots & x & x \\
x & x & 1 & \dots & x & x \\
\vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\
x & x & x & \dots & 1 & x \\
x & x & x & \dots & x & 1 \\
\end{vmatrix} .$$
How to find the (multiple) zeroes, the degree of the polynomial and the initial coefficient, all depending on the natural number $b$?

Add all columns (from second one) to the first one and then substract first row from all the rest:
$$\begin{vmatrix}1+(n-1)x&x&x&\ldots&x\\0&1-x&0&\ldots&0\\0&0&1-x&\ldots&0\\..&..&..&..&..\\0&0&0&\ldots&1-x\end{vmatrix}=\left(1+(n-1)x\right)(1-x)^{n-1}$$
