If y = x^2 + d x + 9 does not cut the x-axis, then which of the follow

Question

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

TeamGMATIFY · Accepted Answer

NOTE:  
 
In the equation  ax^2 = bx + c = 0 
Discriminant =  b^2 - 4ac

Solving an inequality with a less than sign : The value of the variable will be greater than the smaller value and smaller than the greater value i.e. it will between the extremes.

Solving an inequality with a greater than sign : The value of the variable will be smaller than the smaller value and greater than the greater value i.e. it can take all the values except the values in the range.

y = x^2 + d x + 9 does not cut the X-axis, this means that there are no real roots.
If there are no real roots, then Discriminant < 0

Discriminant of the given equation =  d^2 - 4*1*9 = d^2 - 36 
We know that this is < 0
Therefore

d^2 - 36  < 0 or  d^2 < 36 
Hence -6 < d < 6
Therefore d can take the values: 0 and -3

Option C

stonecold · Answer

Here C is the answer as A and B statements will provide the discriminant to be negative thereby making the x axis cutting impossible.
Hence only 1 and 2
thus C

raarun · Answer

-3(minus 3) is not between 0 or 9 and it is also not less that -6.
The answer should be A

rahulkashyap · Answer

Shouldn't the D be <0 if it does not have real roots?

therefore, the answer should be c
as the range becomes -6<x<6

Kurtosis · Answer

Yes I too agree with you. D should be < 0 if the roots are not real.
 Answer has to be C.

stonecold · Answer

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[/quote]

NOTE:

In the equation \(ax^2 = bx + c = 0\)
Discriminant = \(b^2 - 4ac\)

Solving an inequality with a less than sign: The value of the variable will be greater than the smaller value and smaller than the greater value i.e. it will between the extremes.

Solving an inequality with a greater than sign: The value of the variable will be smaller than the smaller value and greater than the greater value i.e. it can take all the values except the values in the range.

y = x^2 + d x + 9 does not cut the X-axis, this means that there are no real roots.
If there are no real roots, then Discriminant > 0

Discriminant of the given equation = \(d^2 - 4*1*9 = d^2 - 36\)
We know that this is > 0
Therefore

\(d^2 - 36\)> 0 or \(d^2 > 36\)
Hence d > 6 or d < -6
Therefore d can take the values: 0 and 9

Option E[/quote]
Shouldn't the D be <0 if it does not have real roots?

therefore, the answer should be c
as the range becomes -6<x<6[/quote]

Yes I too agree with you. D should be < 0 if the roots are not real.
Answer has to be C.[/quote]

AGREED ...!!
Just waiting for the official solution on this one..!!

TeamGMATIFY · Answer

Sorry for the incorrect solution and thanks a lot for pointing it out. I stand corrected guys, might be phased out while solving the question. One incorrect inequality and then solved the whole question considering that equation.
Yes,  if the roots are not real, D < 0

Edited the solution

GMATisLovE · Answer

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

glagad · Answer

I haven't learnt Coordinate Geometry much, so I am not able to comprehend the logic of real vs (un)-real roots.

I wonder if this is a good question to practice for GFE.

The way I solved is - if it doesnt cut x axis, the line represented by the graph, should be parallel to y.

i.e. hence, y = 9, which means x^2 + dx = 0

And Hence C.

bumpbot · Answer

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If y = x^2 + d x + 9 does not cut the x-axis, then which of the follow

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If y = x^2 + d x + 9 does not cut the x-axis, then which of the follow

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