If the three equations x^2 + ax + 12 = 0, x^2 + bx + 15 = 0, and x^2 +
(a+b)x + 36 = 0 have a common positive root, what are the values of a and b? Also, find the roots of the equations.
Options:
A) a = 3, b = 2
B) a = 4, b = 1
C) a = 2, b = 3
D) a = 1, b = 4