Solve for the roots

a²b-3ab=0

The remainder is equal to f(b) by remainder theorem.

f(b)=b

3

−3b

2

.b+3b.b

2

−b

3

=0

Thus it comes out to be 0.

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.