Last visit was: 23 Apr 2026, 20:24 It is currently 23 Apr 2026, 20:24
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: 23 Apr 2026
Posts: 109,785
Own Kudos:
810,878
 [10]
Given Kudos: 105,853
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: 109,785
Kudos: 810,878
 [10]
What is the values of K for which the quadratic equation (K + 4)x^2 + 01 Feb 2021, 10:00
Kudos
Add Kudos
10
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:

71% (01:56) correct 29% (02:24) wrong based on 199 sessions

History

Date
Time
Result
Not Attempted Yet
What is the values of K for which the quadratic equation \((K + 4)x^2 + (K + 1)x + 1 = 0\) has equal roots ?

A. -3 or -5
B. -3 or -1
C. -3 or 1
D. -3 or 5
E. 3 or 5
ShowHide Answer
Official Answer
D
avatar
Aviralft9
avatar
Joined: 11 Sep 2019
Last visit: 15 Oct 2022
Posts: 12
Own Kudos:
21
 [1]
Given Kudos: 30
Location: India
GMAT 1: 700 Q49 V38
GMAT 1: 700 Q49 V38
Posts: 12
Kudos: 21
 [1]
What is the values of K for which the quadratic equation (K + 4)x^2 + 01 Feb 2021, 11:33
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Using the formula b^2 = 4 * a * c, we have,

(K+1)^2 = 4(K+4)
K^2 + 1 + 2K = 4K + 4
K^2 - 2K - 3 = 0
K = 3,-1

No option given, Bunuel, please check the options.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,785
Own Kudos:
810,878
 [1]
Given Kudos: 105,853
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: 109,785
Kudos: 810,878
 [1]
What is the values of K for which the quadratic equation (K + 4)x^2 + 01 Feb 2021, 11:42
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Aviralft9
Using the formula b^2 = 4 * a * c, we have,

(K+1)^2 = 4(K+4)
K^2 + 1 + 2K = 4K + 4
K^2 - 2K - 3 = 0
K = 3,-1

No option given, Bunuel, please check the options.
Show more

Checked. The question is correct. Please try again.
avatar
Aviralft9
avatar
Joined: 11 Sep 2019
Last visit: 15 Oct 2022
Posts: 12
Own Kudos:
21
 [1]
Given Kudos: 30
Location: India
GMAT 1: 700 Q49 V38
GMAT 1: 700 Q49 V38
Posts: 12
Kudos: 21
 [1]
What is the values of K for which the quadratic equation (K + 4)x^2 + 01 Feb 2021, 11:50
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
Aviralft9
Using the formula b^2 = 4 * a * c, we have,

(K+1)^2 = 4(K+4)
K^2 + 1 + 2K = 4K + 4
K^2 - 2K - 3 = 0
K = 3,-1

No option given, Bunuel, please check the options.

Checked. The question is correct. Please try again.
Show more



Sorry, my bad...

(K+1)^2 = 4(K+4)
K^2 + 1 + 2K = 4K + 16
K^2 - 2K - 15 = 0
K = 5, -3

Option D, IMO.
User avatar
Neghineh
User avatar
Joined: 20 Nov 2020
Last visit: 24 Nov 2022
Posts: 28
Own Kudos:
2
Given Kudos: 7
Posts: 28
Kudos: 2
What is the values of K for which the quadratic equation (K + 4)x^2 + 01 Feb 2021, 11:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Could someone please clarify this question more detailed?


(K+1)^2 = 4(K+4) --> I get this
K^2 + 1 + 2K = 4K + 16 (But where does the K^2, the 1, the 1 and the 2k, come from? I cannot figure this out.
avatar
mruffe
avatar
Joined: 22 Nov 2020
Last visit: 01 Feb 2021
Posts: 3
Own Kudos:
1
 [1]
Given Kudos: 5
Posts: 3
Kudos: 1
 [1]
What is the values of K for which the quadratic equation (K + 4)x^2 + 01 Feb 2021, 13:39
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Neghineh
Could someone please clarify this question more detailed?


(K+1)^2 = 4(K+4) --> I get this
K^2 + 1 + 2K = 4K + 16 (But where does the K^2, the 1, the 1 and the 2k, come from? I cannot figure this out.
Show more

(K+1)^2 = (K+1)(K+1)= K^2+K+K+1=K^2+2K+1

Hope it helps
User avatar
r24350
User avatar
Joined: 28 Oct 2015
Last visit: 07 Dec 2023
Posts: 21
Own Kudos:
9
Given Kudos: 48
Location: India
WE:Project Management (Retail Banking)
Posts: 21
Kudos: 9
What is the values of K for which the quadratic equation (K + 4)x^2 + 02 Feb 2021, 23:42
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
What is the values of K for which the quadratic equation \((K + 4)x^2 + (K + 1)x + 1 = 0\) has equal roots ?

A. -3 or -5
B. -3 or -1
C. -3 or 1
D. -3 or 5
E. 3 or 5
Show more


If the question deals with equal roots we can apply the below principle :
the Discriminant has to be equal to zero , since the roots are same .

thus for an equation ax^2 +bx +c , the Discriminant is given by b^2 - 4ac
thus comparing the original condition with the discriminant , we get b = K+1 , a = K+4 , c =1
therefore , (K+1)^2 - 4*(K+4)*1=0
K^2+2K+1 -4K-16=0
k^2 -2K-15=0
K^2 +3K -5K -15 =0 or (K+3)(K-5)=0 , thus K = -3 or 5 IMO ans D
User avatar
m7runner
User avatar
Kellogg School Moderator
Joined: 15 May 2023
Last visit: 22 Apr 2026
Posts: 394
Own Kudos:
49
Given Kudos: 93
Location: India
Schools: Ross '26 (D) Johnson '26 (D) Kellogg '26 (D) McCombs '26 (A$$) Tepper '26 (WL) Foster '26 (A$$) Anderson '26 (D)
GRE 1: Q166 V159
GPA: 7.03
Schools: Ross '26 (D) Johnson '26 (D) Kellogg '26 (D) McCombs '26 (A$$) Tepper '26 (WL) Foster '26 (A$$) Anderson '26 (D)
GRE 1: Q166 V159
Posts: 394
Kudos: 49
What is the values of K for which the quadratic equation (K + 4)x^2 + 10 Jul 2024, 10:25
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
What is the values of K for which the quadratic equation \((K + 4)x^2 + (K + 1)x + 1 = 0\) has equal roots ?

A. -3 or -5
B. -3 or -1
C. -3 or 1
D. -3 or 5
E. 3 or 5
Show more
­
The equation has equal roots; therefore discriminant = 0.

→ \(b^2 - 4ac = 0\)
→ \((K+1)^2 - 4.(K+1).1 = 0\)
Expand to get:
→ \((K-5)(K+3) = 0\)
→ \(K = 5, -3\)
 ­
Moderators:
Bunuel
Math Expert
109785 posts
Krunaal
Tuck School Moderator
853 posts