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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  [#permalink]

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13 Mar 2016, 09:53
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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

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

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Updated on: 18 Mar 2016, 03:40
3
3
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

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

Originally posted by TeamGMATIFY on 15 Mar 2016, 05:27.
Last edited by TeamGMATIFY on 18 Mar 2016, 03:40, edited 1 time in total.
##### General Discussion
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Re: If y = x^2 + d x + 9 does not cut the x-axis, then which of the follow  [#permalink]

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15 Mar 2016, 01:33
1
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
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If y = x^2 + d x + 9 does not cut the x-axis, then which of the follow  [#permalink]

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15 Mar 2016, 05:52
-3(minus 3) is not between 0 or 9 and it is also not less that -6.
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Joined: 09 Oct 2015
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If y = x^2 + d x + 9 does not cut the x-axis, then which of the follow  [#permalink]

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15 Mar 2016, 06:05
TeamGMATIFY wrote:
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

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

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
Marshall & McDonough Moderator
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Posts: 1686
Location: India
Re: If y = x^2 + d x + 9 does not cut the x-axis, then which of the follow  [#permalink]

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15 Mar 2016, 08:09
rahulkashyap wrote:
TeamGMATIFY wrote:
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

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

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

Yes I too agree with you. D should be < 0 if the roots are not real.
Current Student
Joined: 12 Aug 2015
Posts: 2573
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If y = x^2 + d x + 9 does not cut the x-axis, then which of the follow  [#permalink]

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15 Mar 2016, 11:07
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.

AGREED ...!!
Just waiting for the official solution on this one..!!
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If y = x^2 + d x + 9 does not cut the x-axis, then which of the follow  [#permalink]

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18 Mar 2016, 03:42
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
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If y = x^2 + d x + 9 does not cut the x-axis, then which of the follow  [#permalink]

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23 Sep 2017, 07:01
1
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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Re: If y = x^2 + d x + 9 does not cut the x-axis, then which of the follow  [#permalink]

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14 Mar 2019, 11:36
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Re: If y = x^2 + d x + 9 does not cut the x-axis, then which of the follow   [#permalink] 14 Mar 2019, 11:36
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