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

 It is currently 15 Nov 2019, 15:33 ### 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 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8141
GMAT 1: 760 Q51 V42 GPA: 3.82
If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of  [#permalink]

### Show Tags

1
10 00:00

Difficulty:   55% (hard)

Question Stats: 62% (01:40) correct 38% (02:06) wrong based on 130 sessions

### HideShow timer Statistics

If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of m^2+n^2?

A. 10
B. 12
C. 15
D. 24
E. 25

* A solution will be posted in two days.

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8141
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of  [#permalink]

### Show Tags

3
1
==>From x^2-3x-3=(x-m)(x-n)=x^2-(m+n)x+mn, you get m+n=3 and mn=-3. Then you get m^2+n^2=(m+n)^2-2mn=3^2-2*(-3)=15. The answer is C.

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8141
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of  [#permalink]

### Show Tags

1
AK125 wrote:
Can someone post a step by step solution pls...Kudos for this

Hi AK125,

x^2-3x-3=(x-m)(x-n)=x^2-(m+n)x+mn so, m-n=3 and mn=-3

Thank you.
_________________
Manager  B
Joined: 28 Jun 2016
Posts: 206
Concentration: Operations, Entrepreneurship
If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of  [#permalink]

### Show Tags

1
m = x + y

n= x - y

Where x= -b/2a

y= (sqrt(b^2 - 4ac))/2a

m^2+n^2 = 2(x^2 + y^2)

= 2(9/4 + 21/4)

=15

C

Sent from my iPhone using GMAT Club Forum mobile app
Board of Directors D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4832
Location: India
GPA: 3.5
Re: If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of  [#permalink]

### Show Tags

MathRevolution wrote:
If 2 roots of an equation x^2-3x-3 = 0 are m and n, what is the value of m^2+n^2?

A. 10
B. 12
C. 15
D. 24
E. 25

* A solution will be posted in two days.

With acegmat123

That's the perfect and easiest way of solving this question

With (C) hence...

PS : Good question MathRevolution ...
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Intern  Joined: 09 Apr 2016
Posts: 32
Re: If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of  [#permalink]

### Show Tags

Can someone post a step by step solution pls...Kudos for this
Manager  B
Joined: 20 Apr 2014
Posts: 87
Re: If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of  [#permalink]

### Show Tags

It is not clear enough. I miss some step above. please any help ?
Current Student B
Joined: 08 Oct 2016
Posts: 49
Re: If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of  [#permalink]

### Show Tags

MathRevolution wrote:
==>From x^2-3x-3=(x-m)(x-n)=x^2-(m+n)x+mn, you get m+n=3 and mn=-3. Then you get m^2+n^2=(m+n)^2-2mn=3^2-2*(-3)=15. The answer is C.

I don't understand when you solve for (m^2 + n^2) and use (m+n)^2 - 2mn in its place

Posted from my mobile device
Intern  Joined: 09 Apr 2016
Posts: 32
Re: If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of  [#permalink]

### Show Tags

1
gillyelephant wrote:
MathRevolution wrote:
==>From x^2-3x-3=(x-m)(x-n)=x^2-(m+n)x+mn, you get m+n=3 and mn=-3. Then you get m^2+n^2=(m+n)^2-2mn=3^2-2*(-3)=15. The answer is C.

I don't understand when you solve for (m^2 + n^2) and use (m+n)^2 - 2mn in its place

Posted from my mobile device

We do know m+n which equals 3. And we know mn which is -3.

If we square (m+n) -->

(m+n)^2 = m^2 + 2mn + n^2

Plug in what we do know (green):

(3)^2 = m^2 + 2(-3) + n^2
--> 9 = m^2 - 6 + n^2
--> 15 = m^2 + n^2

Hope its clear!
Non-Human User Joined: 09 Sep 2013
Posts: 13585
Re: If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of  [#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 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of   [#permalink] 27 Aug 2018, 16:47
Display posts from previous: Sort by

# If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of  