设这个公共实数根为t,则
t^2 + t + a = 0
t^2 + at + 1 = 0
两式相减得：
（a - 1)t + 1 - a = 0
(a - 1) (t - 1) = 0
t = 1
代回原方程中任一个得： a = -2