does not cut the x

[sanju09]

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


[spoiler]Source: https://gmat-math.blocked/2010/02/4gmat[/spoiler]

[4GMAT_Mumbai]

Hi,

Nice Q ...

The funda is that if the roots of the quad equation are imaginary, then the curve does not touch x-axis.

How do I know if the roots are imaginary? When the Discriminant is -ve.

b^2 - 4ac < 0

d^2 - 4(1)(9) < 0

d^2 < 36.

Hope this helps. Thanks.

[sanju09]

Hi,

Nice Q ...

The funda is that if the roots of the quad equation are imaginary, then the curve does not touch x-axis.

How do I know if the roots are imaginary? When the Discriminant is -ve.

b^2 - 4ac < 0

d^2 - 4(1)(9) < 0

d^2 < 36.

Hope this helps. Thanks.

marvelous, so what is your answer in terms of A-E here?

[idmaa]

Here the correct answer is C ...

D can be both 0 and -3

If D = 0 , x^2 + 9 will always be positive and it will not cut the x-axis

if D = -3 , solving for y=0 will be a imaginary number so it will not cut the x-axis

-Aditya

Hi,

Nice Q ...

The funda is that if the roots of the quad equation are imaginary, then the curve does not touch x-axis.

How do I know if the roots are imaginary? When the Discriminant is -ve.

b^2 - 4ac < 0

d^2 - 4(1)(9) < 0

d^2 < 36.

Hope this helps. Thanks.

marvelous, so what is your answer in terms of A-E here?