We know :
In quadratic equation : ax2 + bx + c = 0
a) Sum of roots = (-b/a)
b) Product of roots = (c/a)
Hence for the equation : x2 +px + 12 = 0 , we are given one root as 4 and c = 12 which is product of the two roots.
Thus the other root = 12 / 4 = 3
==> Sum of roots = 4 + 3 = 7 ==> -p = 7 ==> p = -7
Now for the other given equation : x2 +px + q = 0 , which can be now written as : x2 - 7x + q = 0
It is given that this equation has equal roots .
We know :
For equal roots , we have discriminant " b2 - 4ac = 0"
So here we have :
49 - 4q = 0
==> q = 49 / 4
Hence A) should be the correct option.