Bunuel wrote:

If y = x^2 + d x + 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

The answer is C as follows.

\(x^2 + dx + 9\) is an equation of upward parabola, hence for this equation to not cut x-axis means it should not have any real root.

A quadratic equation do not have any real root when the discriminant (\(b^2 -4ac\)) of the equation is -ve.

So in this case \(b^2 -4ac\)<0 ==> \(d^2 -4*9<0\) ==> \(d^2-36<0\) ==>\(d^2<36\) ==> -6<d<6

Looking at the option only 0 and -3 satisfies this condition.

Hence answer is C (I and II only).

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