A parameter space method for computation of the feasible region of common quadratic Lyapunov function (CQLF) for a class of parameter-dependent switched systems is presented. The existence condition of CQLF is formulated as the solvability condition of a related parametric semi-algebraic system. To this end, a computer algebra method known as Real Root Classification (RRC) technique is utilized. We apply RRC to obtain symbolic conditions to the feasibility of CQLF in the parameter space. Numerical examples demonstrate that our method can compute the feasible region of CQLF without any conservativeness.