Question 2.

It is given that $2^{4x^2} - 2^{2x^2+x+16} + 2^{2x+30} = 0$, which can be written as:

=> $\left(2^{2x^2}\right)^2 - 2^{2x^2} \cdot 2^{x+15} \cdot 2^1 + \left(2^{x+15}\right)^2 = 0$

=> $\left(2^{2x^2} - 2^{x+15}\right)^2 = 0$

=> $2^{2x^2} - 2^{x+15} = 0$ (Since $(a-b)^2 = 0 \Rightarrow a-b = 0$)

=> $2x^2 = x + 15$

=> $2x^2 - x - 15 = 0$

=> $2x^2 - 6x + 5x - 15 = 0$

=> $2x(x-3) + 5(x-3) = 0$

=> $(2x+5)(x-3) = 0$

Hence, the possible values of x are $-\frac{5}{2}$, and 3, respectively.

Therefore, the sum of the possible values is $\left(3 - \frac{5}{2}\right) = \frac{1}{2}$

The correct option is C