does not cut the x

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Thu Aug 26, 2010 8:57 pm

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]

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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Source: Beat The GMAT — Problem Solving | Thu Aug 26, 2010 8:57 pm

4GMAT_Mumbai: Master | Next Rank: 500 Posts; Posts: 161; Joined: Mon Apr 05, 2010 9:06 am; Location: Mumbai; Thanked: 37 times

by 4GMAT_Mumbai » Thu Aug 26, 2010 9:01 pm

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.

Naveenan Ramachandran
4GMAT, Dadar(W) & Ghatkopar(W), Mumbai

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Thu Aug 26, 2010 9:19 pm

4GMAT_Mumbai wrote: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?

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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idmaa: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Thu Sep 11, 2008 3:37 pm; Location: Kuala Lumpur, Malaysia

by idmaa » Thu Aug 26, 2010 11:51 pm

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

sanju09 wrote:
4GMAT_Mumbai wrote: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?

--

Aditya Agarwal

GMAT prep 1 Base Score :- 640 V 27 Q 50
--

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