If a root of the equations ${x^2} - px - 12 = 0$ is 4, While the roots of the equations ${x^2} + px + q = 0$ are same, then the value of q will be

Substituting the root x = 4 into the first equation x^2 - px - 12 = 0 gives 16 - 4p - 12 = 0, so 4p = 4 and p = 1. For the second equation x^2 + px + q = 0 to have equal roots, its discriminant (p^2 - 4q) must be zero. Substituting p = 1 gives 1 - 4q = 0, meaning q = 1/4.

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