Finding determinants of x-loaded matrix?

R friends,

I need to find the determinant of this matrix

x 1 0 0
1 x 1 0
0 1 x 1
0 0 1 x

det yields x^4-3x^2+1

I can then use polyroot to find the roots of the coefficients.

The question is about the use of "x", which is what I'm solving for.

thanks in advance, and this is a back-burner question.

Apologies if I have posted this incorrectly/to the wrong place, I'm a newbie to 
this list...

Robert Gotwals, Chemistry Educator
gotwals at ncssm.edu
The North Carolina School of Science and Mathematics
1219 Broad Street
(919) 416-2774