time complexity

Question

what the time complexity for

T(n)=5T(n/2)+n^2

a.  n

b.n^2

Comments

it will be about O(n^3)

Answer 1

T(n)=5T(n/2)+n^2
Applying master theorem ,
a=5 b=2

f(n)=n²= O(n^log_ba-¢) = O(n^log₂5-1) = O(n²)            Case : 1
So complexity is O(n^log₂5)

Answer 2

master theorem

T(n)=5T(n/2)+n^2

a=5,b=2,K=1,P=0

Case 1: if a>b^k, then T(n)=O(n^logb^a)

                                                            T(n)=O(n^{log₂5 )}