Check out my Math Variety blog posts about how to find the discriminant in a quadratic equation. I have an explanation of what it is, practice problems, and solutions. Click on ads/links of interest and use my search box.
http://mathvariety.blogspot.com/2009/04/discriminant-in-quadratic-equation.html
http://mathvariety.blogspot.com/2009/05/discriminant-in-quadratic-equation.html
http://mathvariety.blogspot.com/2009/05/discriminant-in-quadratic-equation_11.html
The discriminant is b^2-4ac. Here, a=2, b= -6, c=2, so we have:
(-6)^2-4*2*2 which is 36-16 or 20. The answer is b.
The discriminant does not involve a radical sign. Someone who thought the discriminant involves the radical sign might have chosen a) or d) as the answer. This is wrong.