Final answer:
The complexity of the running time function T(n) = n^2 + 6T(n/2) is O(n^(log_2(6))) according to the Master's theorem.
Step-by-step explanation:
To solve the recurrence relation T(n) = n^2 + 6T(n/2) using the Master's theorem, we must compare the function to the standard form T(n) = aT(n/b) + f(n), where a >= 1 and b > 1 are constants, and f(n) is an asymptotically positive function.
In our case, we have a = 6 and b = 2. The f(n) = n^2 part suggests we are dealing with a polynomial, which leads us to consider the three cases of the Master's theorem. We have to compare n^2 to n^(log_b(a)), which is n^(log_2(6)).
Since n^2 grows slower than n^(log_2(6)), we fall into the second case of the Master's theorem. Therefore, the running time function T(n) has a complexity of O(n^(log_2(6))).