Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 28 May 2017, 03:56

### 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

# Events & Promotions

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

# In the equation x^2+bx+12=0, x is a variable and b is a

Author Message
TAGS:

### Hide Tags

Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 633
Followers: 44

Kudos [?]: 973 [0], given: 39

In the equation x^2+bx+12=0, x is a variable and b is a [#permalink]

### Show Tags

21 Feb 2011, 05:38
4
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

66% (01:51) correct 34% (01:24) wrong based on 353 sessions

### HideShow timer Statistics

In the equation x^2+bx+12=0, x is a variable and b is a constant. What is the value of b?

(1) x-3 is a factor of x^2+bx+12.
(2) 4 is a factor of x^2+bx+12=0
[Reveal] Spoiler: OA

_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Last edited by Baten80 on 21 Feb 2011, 06:46, edited 1 time in total.
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2013
Followers: 163

Kudos [?]: 1828 [2] , given: 376

Re: QR:DS 62 Algebra Equation [#permalink]

### Show Tags

21 Feb 2011, 06:18
2
KUDOS
2
This post was
BOOKMARKED
x^2+bx+12=0
a, coefficient of x^2=1
b, coefficient of x=b
c, constant in the quadratic polynomial=12

Let $$\alpha,\beta$$ be the two factors of the equation.

(1) x-3 is a factor of x^2+bx+12.

$$\alpha=3$$
$$\alpha\beta=\frac{c}{a}=\frac{12}{1}$$
$$\beta=\frac{12}{3}=4$$

$$\alpha+\beta=\frac{-b}{a}=\frac{-b}{1}$$
$$b=-7$$
Sufficient.

(2) 4 is a factor of x^2+bx+12=0
Same as statement 1.

$$\beta=4$$
$$\alpha\beta=\frac{c}{a}=\frac{12}{1}$$
$$\alpha=\frac{12}{4}=3$$

$$\alpha+\beta=\frac{-b}{a}=\frac{-b}{1}$$
$$b=-7$$
Sufficient.

Ans: "D"
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 38953
Followers: 7747

Kudos [?]: 106402 [3] , given: 11626

Re: QR:DS 62 Algebra Equation [#permalink]

### Show Tags

21 Feb 2011, 06:40
3
KUDOS
Expert's post
4
This post was
BOOKMARKED
Baten80 wrote:
In the equation x^2+bx+12=0, x is variable and b is a constant. What is the value of b?
(1) x-3 is a factor of x^2+bx+12.
(2) 4 is a root of x^2+bx+12=0

You don't really need Viete's formula for the roots of a quadratic equation.

(1) x-3 is a factor of x^2+bx+12 --> simply means that x=3 is a root of x^2+bx+12=0 (if x-3 is a factor of x^2+bx+12 then x^2+bx+12=(x-3)(x-k)=0, for some k, so x=3 is on of the roots of the equation) --> substitute x=3: 3^2+3b+12=0 --> b=-7. Sufficient.

(2) 4 is a root of x^2+bx+12=0 --> the same here, substitute x=4: 4^2+4b+12=0 --> b=-7. Sufficient.

_________________
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2013
Followers: 163

Kudos [?]: 1828 [0], given: 376

Re: QR:DS 62 Algebra Equation [#permalink]

### Show Tags

21 Feb 2011, 06:56
Bunuel wrote:
Baten80 wrote:
In the equation x^2+bx+12=0, is variable and b is a constant. What is the value of b?
(1) x-3 is a factor of x^2+bx+12.
(2) 4 is a root of x^2+bx+12=0

You don't really need Viete's formula for the roots of a quadratic equation.

(1) x-3 is a factor of x^2+bx+12 --> simply means that x=3 is a root of x^2+bx+12=0 (if x-3 is a factor of x^2+bx+12 then x^2+bx+12=(x-3)(x-k)=0, for some k, so x=3 is on of the roots of the equation) --> substitute x=3: 3^2+3b+12=0 --> b=-7. Sufficient.

(2) 4 is a root of x^2+bx+12=0 --> the same here, substitute x=4: 4^2+4b+12=0 --> b=-7. Sufficient.

Agree!!! This is much easier and way faster than the Viete's formula (I didn't know that's what it's called). Double thanks!!
_________________
Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 633
Followers: 44

Kudos [?]: 973 [0], given: 39

Re: QR:DS 62 Algebra Equation [#permalink]

### Show Tags

21 Feb 2011, 06:59
Bunuel wrote:
Baten80 wrote:
In the equation x^2+bx+12=0, x is a variable and b is a constant. What is the value of b?
(1) x-3 is a factor of x^2+bx+12.
(2) 4 is a factor of x^2+bx+12=0

You don't really need Viete's formula for the roots of a quadratic equation.

(1) x-3 is a factor of x^2+bx+12 --> simply means that x=3 is a root of x^2+bx+12=0 (if x-3 is a factor of x^2+bx+12 then x^2+bx+12=(x-3)(x-k)=0, for some k, so x=3 is on of the roots of the equation) --> substitute x=3: 3^2+3b+12=0 --> b=-7. Sufficient.

(2) 4 is a root of x^2+bx+12=0 --> the same here, substitute x=4: 4^2+4b+12=0 --> b=-7. Sufficient.

First post was wrong. This the correct post.
But I think answer is same.
_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Manager
Joined: 03 Nov 2009
Posts: 65
Followers: 1

Kudos [?]: 14 [0], given: 17

Re: QR:DS 62 Algebra Equation [#permalink]

### Show Tags

21 Feb 2011, 07:16
We could also go by the quadratic extensiosn of the equation :
Since we know it has to have two rootsr Variables -

Statement 1 :-
X^2 - 3x-4x+12 = 0

x(x-3)-4(x-3) = 0

We have two root - X-3 , X-4 , So be has to be -3+-4 = -7 Sufficient

Statement 2:-

Since X = 4 it has be a root X-4, again using the same Expressions as above.

We get B=-7. Sufficient

Ans - D.
Intern
Joined: 26 Feb 2011
Posts: 37
Followers: 1

Kudos [?]: 109 [0], given: 1

### Show Tags

28 Feb 2011, 02:42
In the equation x^2+bx+12=0, x is a variable and b is a constant. What`s the value of b?

1) x-3 is a factor of x^2+bx+12
2) 4 is a root of the equation x^2 + bx + 12=0

Why (1) is sufficient?
Manager
Joined: 14 Feb 2011
Posts: 194
Followers: 4

Kudos [?]: 135 [0], given: 3

Re: In the equation ... [#permalink]

### Show Tags

28 Feb 2011, 02:50
For equation x^2 + bx + 12 = 0, we need to find value of b

1) says x-3 is a factor of x^2+bx+12, or x=3 is one of the roots of this quadratic equation, so 3^2+3b+12 = 0 or 21+3b = 0 or b = -7. Sufficient
2) says 4 is one of the roots so 4^2+4b+12 = 0 or 28+4b = 0 or b = -7. Again sufficient, so D

if x-a is a factor of any polynomial in x, then at x=a, the value of such a polynomial would be 0 or in other words x = a is one of the roots of such a polynomial
Math Expert
Joined: 02 Sep 2009
Posts: 38953
Followers: 7747

Kudos [?]: 106402 [0], given: 11626

Re: In the equation ... [#permalink]

### Show Tags

28 Feb 2011, 03:09
Merging similar topics.
_________________
Director
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 533
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Followers: 3

Kudos [?]: 66 [0], given: 562

Re: In the equation x^2+bx+12=0, x is a variable and b is a [#permalink]

### Show Tags

15 Dec 2012, 23:40
knew that if x-3 is a factor then 3 could be substituted to get x

but did not know the meaning of root thanks..

Bunuel,
is it helpful to memorize viete's formula?
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : http://gmatclub.com/forum/end-of-my-gmat-journey-149328.html#p1197992

Senior Manager
Joined: 25 Mar 2013
Posts: 276
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Followers: 3

Kudos [?]: 29 [0], given: 101

Re: In the equation x^2+bx+12=0, x is a variable and b is a [#permalink]

### Show Tags

03 Oct 2013, 05:49
D...
just find factors, already x-3, x-4 is another factor to get 12 and -3x-4x= -7,
this is possible becz x2+ bx +12 = 0, here b = +/-, to proof equation only is b= -7
_________________

I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you

Intern
Joined: 14 Feb 2012
Posts: 29
Followers: 0

Kudos [?]: 5 [0], given: 6

Re: QR:DS 62 Algebra Equation [#permalink]

### Show Tags

24 Oct 2013, 05:53
Bunuel wrote:
Baten80 wrote:
In the equation x^2+bx+12=0, x is variable and b is a constant. What is the value of b?
(1) x-3 is a factor of x^2+bx+12.
(2) 4 is a root of x^2+bx+12=0

You don't really need Viete's formula for the roots of a quadratic equation.

(1) x-3 is a factor of x^2+bx+12 --> simply means that x=3 is a root of x^2+bx+12=0 (if x-3 is a factor of x^2+bx+12 then x^2+bx+12=(x-3)(x-k)=0, for some k, so x=3 is on of the roots of the equation) --> substitute x=3: 3^2+3b+12=0 --> b=-7. Sufficient.

(2) 4 is a root of x^2+bx+12=0 --> the same here, substitute x=4: 4^2+4b+12=0 --> b=-7. Sufficient.

Im not really following your first point here.

How do you now that x=3 is a root of the equation? If the equation can be factorized in (X+2)(X+6), isn't three then also a factor from the equation?
Math Expert
Joined: 02 Sep 2009
Posts: 38953
Followers: 7747

Kudos [?]: 106402 [0], given: 11626

Re: QR:DS 62 Algebra Equation [#permalink]

### Show Tags

24 Oct 2013, 07:49
waltiebikkiebal wrote:
Bunuel wrote:
Baten80 wrote:
In the equation x^2+bx+12=0, x is variable and b is a constant. What is the value of b?
(1) x-3 is a factor of x^2+bx+12.
(2) 4 is a root of x^2+bx+12=0

You don't really need Viete's formula for the roots of a quadratic equation.

(1) x-3 is a factor of x^2+bx+12 --> simply means that x=3 is a root of x^2+bx+12=0 (if x-3 is a factor of x^2+bx+12 then x^2+bx+12=(x-3)(x-k)=0, for some k, so x=3 is on of the roots of the equation) --> substitute x=3: 3^2+3b+12=0 --> b=-7. Sufficient.

(2) 4 is a root of x^2+bx+12=0 --> the same here, substitute x=4: 4^2+4b+12=0 --> b=-7. Sufficient.

Im not really following your first point here.

How do you now that x=3 is a root of the equation? If the equation can be factorized in (X+2)(X+6), isn't three then also a factor from the equation?

If (x+2)(x+6)=0, then x-3 is NOT a factor of the quadratics. The roots of (x+2)(x+6)=0 are x=-3 and x=-6.

We are told that x-3 is a factor of x^2+bx+12, thus (x-3)(x-k)=0, thus x=3 is one of the roots.

Hope it's clear.
_________________
Intern
Joined: 14 Feb 2012
Posts: 29
Followers: 0

Kudos [?]: 5 [0], given: 6

Re: In the equation x^2+bx+12=0, x is a variable and b is a [#permalink]

### Show Tags

24 Oct 2013, 10:17
Thanks for your response, but I still don't get why x-3 is not a factor.
How can we now for sure that it is not a factor?
Math Expert
Joined: 02 Sep 2009
Posts: 38953
Followers: 7747

Kudos [?]: 106402 [0], given: 11626

Re: In the equation x^2+bx+12=0, x is a variable and b is a [#permalink]

### Show Tags

24 Oct 2013, 10:36
waltiebikkiebal wrote:
Thanks for your response, but I still don't get why x-3 is not a factor.
How can we now for sure that it is not a factor?

How is x-3 a factor of (x+2)(x+6)=0? I has two factors x+2 and x+6.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15495
Followers: 651

Kudos [?]: 210 [0], given: 0

Re: In the equation x^2+bx+12=0, x is a variable and b is a [#permalink]

### Show Tags

27 Dec 2014, 07:50
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.
_________________
Manager
Joined: 14 Jul 2014
Posts: 192
GMAT 1: 600 Q48 V27
GMAT 2: 700 Q49 V35
Followers: 1

Kudos [?]: 14 [0], given: 110

In the equation x^2+bx+12=0, x is a variable and b is a [#permalink]

### Show Tags

27 Dec 2014, 14:40
how can root and factor be the same thing? They are not necessarily the same. Am I wrong? Isn't the second option conveying a different meaning?
Current Student
Status: Applied
Joined: 02 May 2014
Posts: 168
Location: India
Concentration: Operations, General Management
GMAT 1: 690 Q47 V38
GPA: 3.35
WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 34 [0], given: 46

Re: In the equation x^2+bx+12=0, x is a variable and b is a [#permalink]

### Show Tags

28 Dec 2014, 04:22
A tells x-3 a factor means x=3 is a solution so we get value of b...sufficient
B tells 4 is a solution ... hence sufficient.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15495
Followers: 651

Kudos [?]: 210 [0], given: 0

Re: In the equation x^2+bx+12=0, x is a variable and b is a [#permalink]

### Show Tags

23 Apr 2016, 10:39
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.
_________________
Intern
Joined: 26 Aug 2015
Posts: 40
Concentration: Strategy, Economics
GMAT 1: 570 Q40 V28
GMAT 2: 740 Q49 V41
Followers: 0

Kudos [?]: 19 [0], given: 28

In the equation x^2+bx+12=0, x is a variable and b is a [#permalink]

### Show Tags

10 Nov 2016, 10:22
Bunuel wrote:
Baten80 wrote:
In the equation x^2+bx+12=0, x is variable and b is a constant. What is the value of b?
(1) x-3 is a factor of x^2+bx+12.
(2) 4 is a root of x^2+bx+12=0

You don't really need Viete's formula for the roots of a quadratic equation.

(1) x-3 is a factor of x^2+bx+12 --> simply means that x=3 is a root of x^2+bx+12=0 (if x-3 is a factor of x^2+bx+12 then x^2+bx+12=(x-3)(x-k)=0, for some k, so x=3 is on of the roots of the equation) --> substitute x=3: 3^2+3b+12=0 --> b=-7. Sufficient.

(2) 4 is a root of x^2+bx+12=0 --> the same here, substitute x=4: 4^2+4b+12=0 --> b=-7. Sufficient.

Hello Bunuel,

why do you conclude that 4 is a root of the equation if the statement just says it is a factor of (the statement from the page) ... My confusion is that x could be = 12 and 4 would still be a factor of the entire equation.

2) 4 is a factor of $$x^2+bx+12=0$$ ...

if $$x = 12$$, the equation would still be a multiple of 4 and:

$$(12)^2+12b+12=0$$
$$156=-12b$$
$$-13=b$$ which is not $$= -7$$ and therefore it could be "not sufficient". What am I missing?

UPDATE: I looked for the question online and it seems that it has a mistake here, it shouldn't be "factor" ir should say "root". Source:

Please someone correct that, otherwise it is very confusing.
_________________

Send some kudos this way if I was helpful! !

In the equation x^2+bx+12=0, x is a variable and b is a   [#permalink] 10 Nov 2016, 10:22

Go to page    1   2    Next  [ 21 posts ]

Similar topics Replies Last post
Similar
Topics:
6 In the equation x^2 – bx + 4 = 0, x is a variable and b is a constant. 2 20 Feb 2017, 05:23
In the equation x^2 + 5x + k = 0, k is a constant and x is a variable. 1 11 Nov 2016, 03:35
2 In the equation x^2 + bx + 7= 0, where x is a variable, and b is a con 1 24 Aug 2016, 23:29
4 In the equation x^2 + bx + 12 = 0, x is a variable and b is 4 09 Sep 2016, 22:01
5 The variables B and C are functions of the value of A such 4 28 Dec 2014, 04:40
Display posts from previous: Sort by

# In the equation x^2+bx+12=0, x is a variable and b is a

 Powered by phpBB © phpBB Group and phpBB SEO 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®.