GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 25 Feb 2020, 14:16

### 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

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

Author Message
TAGS:

### Hide Tags

Senior Manager
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 398
In the equation x^2+bx+12=0, x is a variable and b is a  [#permalink]

### Show Tags

Updated on: 23 Sep 2018, 19:34
1
18
00:00

Difficulty:

25% (medium)

Question Stats:

72% (01:16) correct 28% (01:43) wrong based on 591 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 root of the equation x^2 + bx + 12 = 0.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/in-the-equat ... 66784.html

_________________

Originally posted by Baten80 on 21 Feb 2011, 04:38.
Last edited by Bunuel on 23 Sep 2018, 19:34, edited 2 times in total.
Math Expert
Joined: 02 Sep 2009
Posts: 61484
Re: In the equation x^2+bx+12=0, x is a variable and b is a  [#permalink]

### Show Tags

21 Feb 2011, 05:40
9
7
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.

_________________
Retired Moderator
Joined: 20 Dec 2010
Posts: 1516
Re: In the equation x^2+bx+12=0, x is a variable and b is a  [#permalink]

### Show Tags

21 Feb 2011, 05:18
3
2
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"
##### General Discussion
Manager
Joined: 14 Feb 2011
Posts: 142
Re: In the equation x^2+bx+12=0, x is a variable and b is a  [#permalink]

### Show Tags

28 Feb 2011, 01:50
1
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
Retired Moderator
Joined: 20 Dec 2010
Posts: 1516
Re: In the equation x^2+bx+12=0, x is a variable and b is a  [#permalink]

### Show Tags

21 Feb 2011, 05:56
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!!
Senior Manager
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 398
Re: In the equation x^2+bx+12=0, x is a variable and b is a  [#permalink]

### Show Tags

21 Feb 2011, 05:59
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.
_________________
Manager
Joined: 03 Nov 2009
Posts: 54
Re: In the equation x^2+bx+12=0, x is a variable and b is a  [#permalink]

### Show Tags

21 Feb 2011, 06:16
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: 29
Re: In the equation x^2+bx+12=0, x is a variable and b is a  [#permalink]

### Show Tags

28 Feb 2011, 01:42
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?
Senior Manager
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 416
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Re: In the equation x^2+bx+12=0, x is a variable and b is a  [#permalink]

### Show Tags

15 Dec 2012, 22:40
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
Manager
Joined: 25 Mar 2013
Posts: 220
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Re: In the equation x^2+bx+12=0, x is a variable and b is a  [#permalink]

### Show Tags

03 Oct 2013, 04:49
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
Intern
Joined: 14 Feb 2012
Posts: 21
Re: In the equation x^2+bx+12=0, x is a variable and b is a  [#permalink]

### Show Tags

24 Oct 2013, 04:53
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: 61484
Re: In the equation x^2+bx+12=0, x is a variable and b is a  [#permalink]

### Show Tags

24 Oct 2013, 06:49
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: 21
Re: In the equation x^2+bx+12=0, x is a variable and b is a  [#permalink]

### Show Tags

24 Oct 2013, 09:17
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: 61484
Re: In the equation x^2+bx+12=0, x is a variable and b is a  [#permalink]

### Show Tags

24 Oct 2013, 09:36
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.
_________________
Manager
Joined: 14 Jul 2014
Posts: 154
Location: United States
Schools: Duke '20 (D)
GMAT 1: 600 Q48 V27
GMAT 2: 720 Q50 V37
GPA: 3.2
Re: In the equation x^2+bx+12=0, x is a variable and b is a  [#permalink]

### Show Tags

27 Dec 2014, 13:40
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?
Manager
Status: Applied
Joined: 02 May 2014
Posts: 117
Location: India
Concentration: Operations, General Management
GMAT 1: 690 Q47 V38
GPA: 3.35
WE: Information Technology (Computer Software)
Re: In the equation x^2+bx+12=0, x is a variable and b is a  [#permalink]

### Show Tags

28 Dec 2014, 03:22
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.
Current Student
Joined: 26 Aug 2015
Posts: 32
Concentration: Strategy, Economics
GMAT 1: 570 Q40 V28
GMAT 2: 740 Q49 V41
Re: In the equation x^2+bx+12=0, x is a variable and b is a  [#permalink]

### Show Tags

10 Nov 2016, 09:22
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.
Board of Directors
Joined: 17 Jul 2014
Posts: 2468
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: In the equation x^2+bx+12=0, x is a variable and b is a  [#permalink]

### Show Tags

09 Mar 2017, 16:42
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

my answer: D, but i guess i got here by lucky chance...

if (x-3) is a factor, then the other one will be (x-4), and b will be -7. sufficient.
i rewrote - if 4 is a factor, then (x-4) is a factor, and so is (x-3), and I can get to b=-7. i guess i was too excited with statement 1...
Math Expert
Joined: 02 Sep 2009
Posts: 61484
Re: In the equation x^2+bx+12=0, x is a variable and b is a  [#permalink]

### Show Tags

03 Jan 2018, 07:44
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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/in-the-equat ... 66784.html
_________________
Re: In the equation x^2+bx+12=0, x is a variable and b is a   [#permalink] 03 Jan 2018, 07:44
Display posts from previous: Sort by