Last visit was: 24 Apr 2026, 08:58 It is currently 24 Apr 2026, 08:58
Home
Messages
Tests
Schools
Events
Close
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
605-655 (Medium)|   Algebra|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,814
Own Kudos:
811,028
 [28]
Given Kudos: 105,871
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,814
Kudos: 811,028
 [28]
If m and n are the roots of the quadratic equation x2 - (2 root 5)x - 13 Mar 2016, 09:58
1
Kudos
Add Kudos
27
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

69% (01:51) correct 31% (02:24) wrong based on 441 sessions

History

Date
Time
Result
Not Attempted Yet
If m and n are the roots of the quadratic equation \(x^2 - (2 \sqrt 5)x - 2 = 0\), the value of \(m^2 + n^2\) is:

A. 18
B. 20
C. 22
D. 24
E. 32
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
TeamGMATIFY
User avatar
Joined: 20 Aug 2015
Last visit: 31 Oct 2016
Posts: 339
Own Kudos:
1,527
 [15]
Given Kudos: 10
Location: India
GMAT 1: 760 Q50 V44
Expert
Expert reply
GMAT 1: 760 Q50 V44
Posts: 339
Kudos: 1,527
 [15]
If m and n are the roots of the quadratic equation x2 - (2 root 5)x - 15 Mar 2016, 05:17
5
Kudos
Add Kudos
10
Bookmarks
Bookmark this Post
Bunuel
If m and n are the roots of the quadratic equation \(x^2 - (2 \sqrt 5)x - 2 = 0\), the value of \(m^2 + n^2\) is:

A. 18
B. 20
C. 22
D. 24
E. 32
Show more

In the equation ax^2 + bx + c =0
Sum of roots = -b/a
Product of roots = c/a

Sum of roots (m + n) = \((2 \sqrt 5)\)
Product of roots (mn) = -2

\(m^2 + n^2\) = \((m + n)^2 - 2mn\) = 20 + 4 = 24
Option D
User avatar
sowragu
User avatar
Joined: 25 Dec 2012
Last visit: 26 Apr 2016
Posts: 103
Own Kudos:
128
 [2]
Given Kudos: 148
Posts: 103
Kudos: 128
 [2]
If m and n are the roots of the quadratic equation x2 - (2 root 5)x - 13 Mar 2016, 10:10
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If m and n are the roots of the quadratic equation \(x^2 - (2 \sqrt 5)x - 2 = 0\), the value of \(m^2 + n^2\) is:

A. 18
B. 20
C. 22
D. 24
E. 32
Show more

Product of root, MN = C/A = -2/1 = -2
Sum of root, M+N = -B/A = -(-2\sqrt{5}/1 )= 2\sqrt{5}

(M+N)^2 = M^2 + N^2 + 2MN = 4*5 = 20

2MN = -2(2) = -4

M^2 + N^2 = 20 + 4 = 24

IMO .D
General Discussion
User avatar
stonecold
User avatar
Joined: 12 Aug 2015
Last visit: 09 Apr 2024
Posts: 2,231
Own Kudos:
3,643
Given Kudos: 893
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Posts: 2,231
Kudos: 3,643
If m and n are the roots of the quadratic equation x2 - (2 root 5)x - 15 Mar 2016, 01:29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Here D = B^2-AC = 28
so the roots are 2√5 +√28/2 and 2√5 -28/2
hence M^2 +N^2 => 28
i.e. D
User avatar
rhine29388
User avatar
Joined: 24 Nov 2015
Last visit: 21 Oct 2019
Posts: 386
Own Kudos:
146
Given Kudos: 231
Location: United States (LA)
Products:
My Reviews
Posts: 386
Kudos: 146
If m and n are the roots of the quadratic equation x2 - (2 root 5)x - 15 Jun 2016, 03:39
Kudos
Add Kudos
Bookmarks
Bookmark this Post
stonecold
Here D = B^2-AC = 28
so the roots are 2√5 +√28/2 and 2√5 -28/2
hence M^2 +N^2 => 28
i.e. D
Show more
Apology for seeing a typo error It should be 24 and not 28.
User avatar
adiagr
User avatar
Joined: 18 Jan 2010
Last visit: 05 Oct 2019
Posts: 202
Own Kudos:
1,155
 [1]
Given Kudos: 9
GMAT 1: 710 Q48 V40
Posts: 202
Kudos: 1,155
 [1]
If m and n are the roots of the quadratic equation x2 - (2 root 5)x - 15 Jun 2016, 04:12
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
If m and n are the roots of the quadratic equation \(x^2 - (2 \sqrt 5)x - 2 = 0\), the value of \(m^2 + n^2\) is:

A. 18
B. 20
C. 22
D. 24
E. 32
Show more

m+n = -{- (2 \sqrt 5)}
mn = -2

Squaring 1st equation we get

\(m^2+n^2+2mn = 20\)

\(m^2+n^2= 20 - 2 *(-2)\)

\(m^2+n^2= 20 + 4\) = 24

D is the answer.
User avatar
jfranciscocuencag
User avatar
Joined: 12 Sep 2017
Last visit: 17 Aug 2024
Posts: 227
Own Kudos:
144
 [1]
Given Kudos: 132
Posts: 227
Kudos: 144
 [1]
If m and n are the roots of the quadratic equation x2 - (2 root 5)x - 25 Feb 2019, 19:53
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
TeamGMATIFY
Bunuel
If m and n are the roots of the quadratic equation \(x^2 - (2 \sqrt 5)x - 2 = 0\), the value of \(m^2 + n^2\) is:

A. 18
B. 20
C. 22
D. 24
E. 32

In the equation ax^2 + bx + c =0
Sum of roots = -b/a
Product of roots = c/a

Sum of roots (m + n) = \((2 \sqrt 5)\)
Product of roots (mn) = -2

\(m^2 + n^2\) = \((m + n)^2 - 2mn\) = 20 + 4 = 24
Option D
Show more

Hello!

Could someone please clarify to me why \(m^2 + n^2\) is the same as:

\(m^2 - 2mn + n^2\)

Kind regards!
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 24 Apr 2026
Posts: 22,283
Own Kudos:
26,534
 [1]
Given Kudos: 302
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 22,283
Kudos: 26,534
 [1]
If m and n are the roots of the quadratic equation x2 - (2 root 5)x - 02 Mar 2019, 10:11
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
If m and n are the roots of the quadratic equation \(x^2 - (2 \sqrt 5)x - 2 = 0\), the value of \(m^2 + n^2\) is:

A. 18
B. 20
C. 22
D. 24
E. 32
Show more

For any quadratic equation of the form x^2 + bx + c = 0, if r and s are the roots of the equation, then r + s = -b and rs = c. So here we have:

m + n = 2√5 and mn = -2

Squaring the first equation, we have:

(m + n)^2 = (2√5)^2

m^2 + 2mn + n^2 = 20

Since mn = -2, we have:

m^2 + 2(-2) + n^2 = 20

m^2 - 4 + n^2 = 20

m^2 + n^2 = 24

Answer: D
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,974
Own Kudos:
1,117
Posts: 38,974
Kudos: 1,117
If m and n are the roots of the quadratic equation x2 - (2 root 5)x - 28 Nov 2025, 12:21
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109814 posts
Krunaal
Tuck School Moderator
853 posts