(Solved): Find the solution to the following linear, homogeneous recurrence with constant coefficients: an ...

Find the solution to the following linear, homogeneous recurrence with constant coefficients: $a_n=2a_{n?1}?5a_{n?2}$ for $n?2$ with initial conditions $a_0=?10,a_1=6$. The solution is of the forr $a_n=(?+i?)(r+is{)}^n+(??i?)(r?is{)}^n$ for suitable real constants $?,?,r,s$. Note that the variable $r$ in this problem doesn't represent a characteristic value. Find these constants and enter their values: $\begin{array}{l}r=\\ s=\\ ?=\end{array}$