A cubic equation can be expressed in terms of its roots as

$x^3$-(sum of the roots) $x^2$+(sum of the product of the roots taken 2 at a time) x-(product of the roots)=0

thus,

p= sum of roots taken one at a time

q= sum of roots taken two at a time

Product of roots =8 (given in question)

 'if the product of 2 or more numbers is constant, the sum will be minimum when they are equal'

i.e.If abc=constant, the minimum value of a+b+c will be obtained at a=b=c

Thus, For the sum of roots (p) to be minimum, 8 should be the product of 3 numbers that are equal to each other (difference between them should be equal). This number is 2. The roots are thus 2,2,2

P= 2+2+2= 6

And q= 2(2)+2(2)+2(2)= 12

Answer= option b