How can we get a compact form of the Eigenvalues?

Question

I want to get a compact form of the eigenvalues of this matrix

Eigenvalues[({
   {-r,  p1, 0, 0},
   {p1, -r, 1, 0},
   {0, 1, r,  p2},
   {0, 0, p2, r}
  })]   

this is the output

{Root[p1^2 p2^2 + r^2 - p1^2 r^2 - p2^2 r^2 + 
    r^4 + (2 p1^2 r - 2 p2^2 r) #1 + (-1 - p1^2 - p2^2 - 
       2 r^2) #1^2 + #1^4 &, 1], 
 Root[p1^2 p2^2 + r^2 - p1^2 r^2 - p2^2 r^2 + 
    r^4 + (2 p1^2 r - 2 p2^2 r) #1 + (-1 - p1^2 - p2^2 - 
       2 r^2) #1^2 + #1^4 &, 2], 
 Root[p1^2 p2^2 + r^2 - p1^2 r^2 - p2^2 r^2 + 
    r^4 + (2 p1^2 r - 2 p2^2 r) #1 + (-1 - p1^2 - p2^2 - 
       2 r^2) #1^2 + #1^4 &, 3], 
 Root[p1^2 p2^2 + r^2 - p1^2 r^2 - p2^2 r^2 + 
    r^4 + (2 p1^2 r - 2 p2^2 r) #1 + (-1 - p1^2 - p2^2 - 
       2 r^2) #1^2 + #1^4 &, 4]}

How can I understand this output and what is #1?

is it possible to simplify and get a compact form knowing that all elements of the matrix are real?