Question: help with solving determinants

I trying to solve the following matrix

A:=Matrix([[alpha_O-E, beta_CO, 0, 0],[beta_CO, alpha_C-E, beta_CC, 0],[0, beta_CC, alpha_C-E, beta_CC],[0, 0, beta_CC, alpha_C-E]]);

by setting the determinant to zero and finding the roots in terms of parameters alpha_O, beta_CO, alpha_C, and beta_CC.  I have tried to use solve which returns

           4                            3
  RootOf(_Z  + (-alpha_O - 3 alpha_C) _Z  +

                                      2            2          2    2
        (3 alpha_O alpha_C + 3 alpha_C  - 2 beta_CC  - beta_CO ) _Z

                              2                    2          3
         + (-3 alpha_O alpha_C  + 2 alpha_O beta_CC  - alpha_C

                            2            2
         + 2 alpha_C beta_CC  + 2 beta_CO  alpha_C) _Z

                          3          2        2
         + alpha_O alpha_C  + beta_CO  beta_CC

                                    2          2        2
         - 2 alpha_O alpha_C beta_CC  - beta_CO  alpha_C )

Any suggestions would be greatly appreciated.