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

 It is currently 29 Jan 2020, 04:09 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If (x−2√3) is one factor of the equation x^2+(4√3)·x−36=0,

Author Message
TAGS:

### Hide Tags

Intern  Joined: 28 Jan 2013
Posts: 1
If (x−2√3) is one factor of the equation x^2+(4√3)·x−36=0,  [#permalink]

### Show Tags

10 00:00

Difficulty:

(N/A)

Question Stats: 68% (01:35) correct 32% (01:38) wrong based on 241 sessions

### HideShow timer Statistics

If (x−2√3) is one factor of the equation x^2+(4√3)·x−36=0, what is the other factor of the equation?\

A. (x+2√3)
B. (x+4√3)
C. (x+6√3)
D. (x−2√3)
E. (x−6√3)

I tried to solve the equation by putting the value of x as (x−2√3) and got x= √48..and then I just got confused Can someone tell me the correct approach to the problem?

Thanks

Originally posted by bzb on 25 Sep 2013, 10:59.
Last edited by Bunuel on 25 Sep 2013, 11:08, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert V
Joined: 02 Sep 2009
Posts: 60772
Re: If (x−2√3) is one factor of the equation x^2+(4√3)·x−36=0,  [#permalink]

### Show Tags

3
5
bzb wrote:
If (x−2√3) is one factor of the equation x^2+(4√3)·x−36=0, what is the other factor of the equation?\

A. (x+2√3)
B. (x+4√3)
C. (x+6√3)
D. (x−2√3)
E. (x−6√3)

I tried to solve the equation by putting the value of x as (x−2√3) and got x= √48..and then I just got confused Can someone tell me the correct approach to the problem?

Thanks

Viete's theorem states that for the roots $$x_1$$ and $$x_2$$ of a quadratic equation $$ax^2+bx+c=0$$:

$$x_1+x_2=\frac{-b}{a}$$ AND $$x_1*x_2=\frac{c}{a}$$.

So, we know that one of the roots of $$x^2+(4\sqrt{3})x-36=0$$ is $$2\sqrt{3}$$.

According to the theorem above $$2\sqrt{3}*x_2=\frac{c}{a}=\frac{-36}{1}$$ --> $$x_2=-\frac{18}{\sqrt{3}}=-6\sqrt{3}$$.

_________________
##### General Discussion
SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1721
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If (x−2√3) is one factor of the equation x^2+(4√3)·x−36=0,  [#permalink]

### Show Tags

Basic Formula:

(x+a) * (x+b) = x^2 + (a+b) * x + ab

Given equation:

$$x^2 + 4\sqrt{3} x - 36 = 0$$; one of the root = $$x - 2\sqrt{3}$$

Just observe & try to compare with the basic formula

1. Highlighted sign in the equation is +ve & middle sign of the root is -ve.

It means middle sign of the other root has to be +ve

Re-writing the equation as follow:

$$x^2 + (6\sqrt{3} - 2\sqrt{3}) x - (6\sqrt{3} * 2\sqrt{3}) = 0$$

$$x(x + 6\sqrt{3}) - 2\sqrt{3} (x + 6\sqrt{3}) = 0$$

$$(x + 6\sqrt{3}) (x - 2\sqrt{3}) = 0$$

$$Other root = x + 6\sqrt{3}$$

Intern  B
Joined: 07 Feb 2016
Posts: 11
GMAT 1: 710 Q47 V40
Re: If (x−2√3) is one factor of the equation x^2+(4√3)·x−36=0,  [#permalink]

### Show Tags

We don't really need Viete's theorem to solve this problem. We know that C=-36, so the second factor will be (x+k) for some number k. You can scratch D and E already. Now, the simple equation is -2√3 * k = -36. So K= -36/-2√3 --->6√3
Non-Human User Joined: 09 Sep 2013
Posts: 14002
Re: If (x−2√3) is one factor of the equation x^2+(4√3)·x−36=0,  [#permalink]

### Show Tags

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.
_________________ Re: If (x−2√3) is one factor of the equation x^2+(4√3)·x−36=0,   [#permalink] 11 Dec 2017, 03:33
Display posts from previous: Sort by

# If (x−2√3) is one factor of the equation x^2+(4√3)·x−36=0,  