If $$a \in R$$, then the equation $$x^2 + x + a = 0$$ and $$x^2 + ax + 1 = 0$$ have a common real root for

Let '$$\alpha$$' be the common root that satisfies both equations.
Putting $$\alpha$$ into both equations gives:

$$\Rightarrow$$ $$\alpha^{2}$$ + $$\alpha$$ + a $$=0$$ --- 1st eq

$$\Rightarrow$$ $$\alpha^{2}$$ + a$$\alpha$$ + $$1 = 0$$ --- 2nd eq
On subtracting the 2nd equation from the 1st, we get:

$$\Rightarrow$$ ($$\alpha^{2}$$ + $$\alpha$$ + a) -($$\alpha^{2}$$ + a$$\alpha$$ + $$1$$) $$=0$$

$$\Rightarrow$$ $$\alpha$$(1-a)$$=1-$$a

$$\Rightarrow$$ $$\alpha = 1$$
Substituting the value of $$\alpha$$ in any of the equations, we get a$$=-2$$

Only the range in Option C is satisfied. Hence, Option C is correct.