We know :

In quadratic equation : ax^{2} + bx + c = 0

a) Sum of roots = (-b/a)

b) Product of roots = (c/a)

Hence for the equation : x^{2} +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 : x^{2} +px + q = 0 , which can be now written as : x^{2} - 7x + q = 0

It is given that this equation has equal roots .

We know :

For equal roots , we have discriminant " b^{2} - 4ac = 0"

So here we have :

49 - 4q = 0

**==> q = 49 / 4**

**Hence A) should be the correct option.**