If 2 is a root of the equation x2 + bx + 12 = 0 and the equation x2 + bx + q = 0 has equal roots, then q =
2 is the root of given equation x2 + bx + 12 = 0
So 22 + 2b + 12 = 0
16 + 2b = 0
b = – 8…………..1
Now, d = b2 – 4ac = 0 of second equation is
d = b2 – 4 (1) (q) = 0 here a = 1, b = – 8 (from 1) and c = q
(– 8)2 – 4q = 0
64 – 4q = 0
q = 16
Hence value of q is 16.