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If y = x^2 + dx + 9 does not cut the x-axis, then which of the following could be a possible value of d?
I. 0
II. -3
III. 9

A. III only
B. II only
C. I and II only
D. II and III only
E. I and III only

Is 'C' the answer?

Get imaginary roots when d = 0 or d = -3. So, it cannot cut the x-axis for those values of d.

You are right.

for values of -6 < d < 6, one will get imaginary roots.

A detailed explanation is given at http://gmat-math.blogspot.com/2009/07/g ... abola.html