# Expanding a large dynamic expression involving roots of a degree 4 polynomial

I am trying to find the eigenvalues of a 4x4 Matrix symbolically. Below is the code I am using,

P = (3 Subscript[a, 0]^2 - 125)/(Subscript[a, 0]^2 + 25);
Q = (20 Subscript[a, 0])/(Subscript[a, 0]^2 + 25);
R = (2 Subscript[a, 0]^2 Subscript[b, 0 ] c)/(
Subscript[a, 0]^2 + 25);
S = (5  Subscript[a, 0] Subscript[b, 0 ] c)/(Subscript[a, 0]^2 + 25);
Subscript[\[Theta], 1] = (2 Subscript[a, 0]^2 c)/(
Subscript[a, 0]^2 + 25);
Subscript[\[Theta], 2] = (5 Subscript[a, 0] c)/(
Subscript[a, 0]^2 + 25);
M = ( {
{P, Q, 0, 0},
{R, S, Subscript[\[Theta], 1], Subscript[\[Theta], 2]},
{0, 0 , P - \[Lambda], Q},
{\[Sigma] Subscript[\[Theta], 1], \[Sigma] Subscript[\[Theta], 2],
R, S - \[Lambda]}
} );
x = Eigenvalues[M];

The element e1 represents the first eigenvalue of the matrix; I want it in the form of nested radicals instead of the Root function.Thus I have used the ToRadicals command.
• Possibly e1 = x[[1]] // ToRadicals // StandardForm will do what you want. Commented Jan 26, 2023 at 21:34