I easily can guess:  the roots 2 and 4 gives the product of 8 (the constant term) and the difference of 2.


Their sum is 6, which should be " q", according to Vieta's theorem.


So, the answer is q = 6, based on my guessing.



Let's look what the Algebra solution will give us.


Let x and (x-2) are the roots.

Then their product is 8:

    x*(x-2) = 8

    x^2 - 2x - 8 = 0

    (x-4)*(x+2) = 0.


So, there are 2 roots:  x= 4  and  x= -2.


The value  x= 4  gives that two roots  4 and 2 which I guessed above, with the value  of q= 6.


The value x= -2 gives two roots  -2 and -4, with the value of q = -6.


So, the problem has two answers:  q= 6  and  q= -6.    (Third line of the answers' choice)