GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Sep 2018, 10:05

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# For integers x, b and c, x^2 + bx + c = 0. Is x > 0?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49303
For integers x, b and c, x^2 + bx + c = 0. Is x > 0?  [#permalink]

### Show Tags

09 Feb 2017, 01:23
1
1
00:00

Difficulty:

55% (hard)

Question Stats:

59% (01:10) correct 41% (01:09) wrong based on 114 sessions

### HideShow timer Statistics

For integers x, b and c, x^2 + bx + c = 0. Is x > 0?

(1) b > 0
(2) c > 0

_________________
SC Moderator
Joined: 13 Apr 2015
Posts: 1703
Location: India
Concentration: Strategy, General Management
GMAT 1: 200 Q1 V1
GPA: 4
WE: Analyst (Retail)
Re: For integers x, b and c, x^2 + bx + c = 0. Is x > 0?  [#permalink]

### Show Tags

09 Feb 2017, 09:42
x^2 + bx + c = 0 can have two roots x1 and x2

Sum of the roots = x1 + x2 = -b
Product of the roots =x1 * x2 = c

St1: b > 0 --> x1 + x2 is negative. Cannot determine if the roots are positive or negative.
Not Sufficient.

St2: c > 0 --> x1 * x2 is positive --> Both the roots are either positive or negative.
Not Sufficient.

Combining St1 and St2,
x1 + x2 = negative and x1 * x2 = positive --> Both the roots have to be negative.
Sufficient.

PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1214
Location: India
GPA: 3.82
Re: For integers x, b and c, x^2 + bx + c = 0. Is x > 0?  [#permalink]

### Show Tags

15 Feb 2018, 10:51
Bunuel wrote:
For integers x, b and c, x^2 + bx + c = 0. Is x > 0?

(1) b > 0
(2) c > 0

One of the method is to use the properties of roots of a quadratic equation that has already been explained in the earlier post. We can also solve this question logically.

as $$x^2 + bx + c = 0$$ and $$x^2$$ is always positive so the summation to be $$0$$ either both $$bx+c$$ is negative with magnitude equal to $$x^2$$ or either of $$bx$$ or $$c$$ is negative.

Statement 1: given $$b>0$$, if $$c>0$$ then $$x<0$$ but if $$c<0$$ then $$x>0$$ or $$x<0$$. Hence multiple scenarios possible. Insufficient

Statement 2: given $$c>0$$, if $$b>0$$ then $$x<0$$ and if $$b<0$$ then $$x>0$$. Again multiple scenarios possible. Insufficient

Combining 1 & 2: $$b>0$$ & $$c>0$$, hence $$x<0$$ . Sufficient

Option C
Re: For integers x, b and c, x^2 + bx + c = 0. Is x > 0? &nbs [#permalink] 15 Feb 2018, 10:51
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.