If y = x

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

Correct Answer : Choice C. Values that 'd' could take are 0 or -3

Explanation

The question states that the curve (parabola) does not cut the x-axis.

If y = x

As any point on the x-axis will be a value on the number line, the roots will be real numbers.

However, if the curve does not cut the x-axis, then roots of the quadratic equation will be imaginary.

For a quadratic equation "ax

In this equation, d

Or d

i.e., -6 < d < 6.

Amongst the values given, d = 0 and d = -3 lie in this range.

Hence, choice C.

Labels: GMAT Quadratic Equations, GMAT Roots of Equations, imaginary roots, Parabola, real roots