It is currently 19 Nov 2017, 01:54

### 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
Your Progress

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ?

 post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 12 Feb 2006
Posts: 26

Kudos [?]: 13 [0], given: 0

If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ? [#permalink]

### Show Tags

19 May 2006, 11:27
1
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

51% (01:04) correct 49% (01:10) wrong based on 140 sessions

### HideShow timer Statistics

If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ?

(1) a = 1
(2) b = 2

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-2-3x-c-x-a-x-b-for-all-x-what-is-the-105824.html
[Reveal] Spoiler: OA

Kudos [?]: 13 [0], given: 0

Manager
Joined: 14 Mar 2006
Posts: 208

Kudos [?]: 10 [0], given: 0

Re: If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ? [#permalink]

### Show Tags

19 May 2006, 11:43
C?

by subing both a and b. we get :

x^2 +3x + 2

set both sides equal and solve for c.

Kudos [?]: 10 [0], given: 0

Director
Joined: 16 Aug 2005
Posts: 937

Kudos [?]: 30 [1], given: 0

Location: France
Re: If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ? [#permalink]

### Show Tags

19 May 2006, 11:48
1
This post received
KUDOS
x^2 + ax+bx + ab
a+b=3
c=ab

hence D

Kudos [?]: 30 [1], given: 0

Manager
Joined: 13 Dec 2005
Posts: 224

Kudos [?]: 8 [0], given: 0

Location: Milwaukee,WI
Re: If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ? [#permalink]

### Show Tags

19 May 2006, 11:49
1
This post was
BOOKMARKED
yach wrote:
If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ?
(1) a = 1
(2) b = 2

Please explain your answer. Thanks

It should be D

equation both the equation we get

x^2 + 3x + c = x^2 + (a+b)x + ab

which means a +b =3 and ab =c

from condition 1 we know a =1 so b =2 so c =2 sufficient
from condition 2 we know b =2 so a =1 so c =2 sufficient

hence D

Kudos [?]: 8 [0], given: 0

VP
Joined: 29 Dec 2005
Posts: 1337

Kudos [?]: 69 [0], given: 0

Re: If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ? [#permalink]

### Show Tags

19 May 2006, 12:00
yach wrote:
If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ?
(1) a = 1
(2) b = 2

x^2 + 3x + c = (x + a)(x + b)
x^2 + 3x + c = x^2 + xa + x b + ab
3x + c = x(a + b) + ab

here 3x = x(a + b) or a+b = 3, and c = ab
now each of the statement is suffcient to find the value of c.

so D.

Kudos [?]: 69 [0], given: 0

Manager
Joined: 14 Mar 2006
Posts: 208

Kudos [?]: 10 [0], given: 0

Re: If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ? [#permalink]

### Show Tags

19 May 2006, 12:39
I think I am getting worse in math day by day
Have exam on May 30th. good luck to me

Kudos [?]: 10 [0], given: 0

Non-Human User
Joined: 09 Sep 2013
Posts: 15706

Kudos [?]: 282 [0], given: 0

Re: If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ? [#permalink]

### Show Tags

22 Jul 2015, 23:59
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 282 [0], given: 0

Intern
Joined: 22 Jul 2015
Posts: 10

Kudos [?]: 1 [0], given: 37

Re: If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ? [#permalink]

### Show Tags

23 Jul 2015, 01:53
yach wrote:
If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ?
(1) a = 1
(2) b = 2

Please explain your answer. Thanks

Here, x^2 +3x +c=(x+a)(x+c)
or, x^2 +3x +c =x^2+x(a+b)+ab
or,3x+c=x(a+b)+ab
Now you can tell 3x = x(a+b), so c=ab

From statement 1, you never get the value of b. so it is insufficient.
From statement 2, you never get the value of a. so it is insufficient.
From the both statements you get the value of both a &b. so it is sufficient. a=1 & b=2 and ab=2
Again your taken condition 3x= x(a+b) is also fulfilled. just like 3x= x(1+2).
Thank you

Kudos [?]: 1 [0], given: 37

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132646 [0], given: 12326

Re: If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ? [#permalink]

### Show Tags

23 Jul 2015, 02:37
yach wrote:
If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ?

(1) a = 1
(2) b = 2

Since $$x^2+3x+c=(x + a)(x + b)$$ is true "for ALL values of $$x$$" then it must hold true for $$x=0$$ too --> $$c=ab$$;

Next, substitute $$c=ab$$ --> $$x^2+3x+ab=x^2+bx+ax+ab$$ --> $$3x=bx+ax$$ --> again it must be true for $$x=1$$ too --> $$a+b=3$$.

So we have: $$c=ab$$ and $$a+b=3$$. Question: $$c=?$$

(1) $$a=1$$ --> as $$a+b=3$$ then $$b=2$$ and $$c=ab=2$$. Sufficient
(2) $$b=2$$ --> as $$a+b=3$$ then $$a=1$$ and $$c=ab=2$$. Sufficient.

Answer: D.

Similar questions:
equation-ds-105823.html?hilit=constants#p768377
equating-coefficients-in-a-quadratic-equation-103919.html

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-2-3x-c-x-a-x-b-for-all-x-what-is-the-105824.html
_________________

Kudos [?]: 132646 [0], given: 12326

Re: If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ?   [#permalink] 23 Jul 2015, 02:37
Display posts from previous: Sort by

# If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ?

 post reply Question banks Downloads My Bookmarks Reviews Important topics

 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®.