The common root of $$x^2 + 10x + 24 = 0$$ and $$x^2 + 14x + 48 = 0$$ is:

For the common roots, the first approach shall be to find the common points of the two equations and see if it is the root for both of them. If not, then solve the equations independently and check for the common root. 

Using the first approach, $$x^2 + 10x + 24$$ = $$x^2 + 14x + 48$$, we get x as -6 for the common point. 

On substituting this in each of the equations, we find that it is a root to both the equations, and hence the answer.