Last visit was: 11 Dec 2024, 17:35 It is currently 11 Dec 2024, 17:35
Home
GMAT
Messages
Tests
Schools
Reviews
Social
Chat
My Profile
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
555-605 Level|   Algebra|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 Dec 2024
Posts: 97,815
Own Kudos:
685,149
 [5]
Given Kudos: 88,242
Products:
GMAT Club Tests Forum Quiz
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 97,815
Kudos: 685,149
 [5]
Let f(x) = x^2 + bx + c. If f(6) = 0 and f(-3) = 0, then b + c = 06 Nov 2014, 09:23
Kudos
Add Kudos
5
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:

25% (medium)

Question Stats:

79% (02:06) correct 21% (02:27) wrong based on 323 sessions

History

Date
Time
Result
Not Attempted Yet

Tough and Tricky questions: Algebra.



Let f(x) = x^2 + bx + c. If f(6) = 0 and f(-3) = 0, then b + c =

A. 18
B. 15
C. -15
D. -21
E. -24

Kudos for a correct solution.
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
Gnpth
User avatar
Joined: 29 Aug 2012
Last visit: 03 Mar 2023
Posts: 1,052
Own Kudos:
6,472
 [6]
Given Kudos: 330
Status:Chasing my MBB Dream!
Location: United States (DC)
WE:General Management (Aerospace and Defense)
Products:
My Reviews
Posts: 1,052
Kudos: 6,472
 [6]
Let f(x) = x^2 + bx + c. If f(6) = 0 and f(-3) = 0, then b + c = 06 Nov 2014, 09:38
5
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
f(x) = x^2 + bx + c. If f(6) = 0 and f(-3) = 0, then b + c =

f(6) = 0= 36+6b+c--- Taking 36 to the other side

-> 6b+c= -36

f(-3) = 0= 9-3b+c --- taking -3b+c to the other side

-> 3b-c=9

When we add these 2 equations, we get 9b= -27---> b= -3

And while substituting b= -3 we get c= -18.

b+c= -21--- Answer D
General Discussion
avatar
PareshGmat
avatar
Joined: 27 Dec 2012
Last visit: 10 Jul 2016
Posts: 1,551
Own Kudos:
7,512
 [3]
Given Kudos: 193
Status:The Best Or Nothing
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Posts: 1,551
Kudos: 7,512
 [3]
Let f(x) = x^2 + bx + c. If f(6) = 0 and f(-3) = 0, then b + c = 10 Nov 2014, 01:37
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
\(f(x) = x^2 + bx + c\)

f(6) = 36 + 6b + c = 0

f(-3) = 9 - 3b + c = 0

c = -18; b = -3

b+c = -18-3 = -21

Answer = D
User avatar
Temurkhon
User avatar
Joined: 23 Jan 2013
Last visit: 06 Apr 2019
Posts: 417
Own Kudos:
278
Given Kudos: 43
Schools: Cambridge'16
Schools: Cambridge'16
Posts: 417
Kudos: 278
Let f(x) = x^2 + bx + c. If f(6) = 0 and f(-3) = 0, then b + c = 17 Aug 2015, 06:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
6 and -3 are roots of quadratic equation x^2+bx+c=0

c=6*(-3)= -18
b=6+(-3)=3*-1=-3
b+c=-18+(-3)=-21

D
User avatar
CareerGeek
User avatar
Joined: 20 Jul 2017
Last visit: 10 Dec 2024
Posts: 1,297
Own Kudos:
3,781
 [1]
Given Kudos: 162
Location: India
Concentration: Entrepreneurship, Marketing
GMAT 1: 690 Q51 V30
WE:Education (Education)
GMAT 1: 690 Q51 V30
Posts: 1,297
Kudos: 3,781
 [1]
Let f(x) = x^2 + bx + c. If f(6) = 0 and f(-3) = 0, then b + c = 19 Jun 2019, 10:46
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

Tough and Tricky questions: Algebra.



Let f(x) = x^2 + bx + c. If f(6) = 0 and f(-3) = 0, then b + c =

A. 18
B. 15
C. -15
D. -21
E. -24

Kudos for a correct solution.

f(6) = 0
—> 6^2 + b(6) + c = 0
—> 36 + 6b + c = 0
—> 6b + c = -36 ...... (1)

and f(-3) = 0
—> (-3)^2 + b(-3) + c = 0
—> 9 - 3b + c = 0
—> -3b + c = -9 ....... (2)

(1) - (2) gives
—> 6b + c - (-3b + c) = -36 - (-9)
—> 9b = -27
—> b = -3

Substitute in (1)
—> 6(-3) + c = -36
—> c = -18

So, b + c = -3 + (-18) = -21


Alternative Method:

f(6) = 0 and f(-3) = 0
—> Roots of the given quadratic equation are 6 & -3

So, the quadratic equation is (x - 6)(x + 3) = 0
—> x^2 - 3x - 18 = 0
Compare the above with given equation x^2 + bx + c = 0
—> b = -3 & c = -18
So, b + c = -3 + (-18) = -21

IMO Option C

Pls Hit kudos if you like the solution

Posted from my mobile device
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 11 Dec 2024
Posts: 19,854
Own Kudos:
24,260
Given Kudos: 288
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 19,854
Kudos: 24,260
Let f(x) = x^2 + bx + c. If f(6) = 0 and f(-3) = 0, then b + c = 23 Jun 2019, 19:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

Tough and Tricky questions: Algebra.



Let f(x) = x^2 + bx + c. If f(6) = 0 and f(-3) = 0, then b + c =

A. 18
B. 15
C. -15
D. -21
E. -24

Kudos for a correct solution.

Since f(6) = 0:

36 + 6b + c = 0

c = -6b - 36

Since f(-3) = 0

9 - 3b + c = 0

c = 3b - 9

Setting the two values for c equal:

-6b - 36 =3b - 9

-27 = 9b

-3 = b

Thus, c = -6(-3) - 36 = 18 - 36 = -18

So, b + c = -3 + -18 = -21
Alternate solution:

Since f(6) = 0 and f(-3) = 0, the equation x^2 + bx + c = 0 can be factored as (x - 6)(x + 3) = 0. Expand (x - 6)(x + 3) = 0, we have x^2 - 3x - 18 = 0. We see that b must be -3 and c must be -18. Therefore, b + c = -3 + (-18) = -21.

Answer: D
avatar
GMATINSECT
avatar
Joined: 17 Jun 2017
Last visit: 22 Jul 2020
Posts: 57
Own Kudos:
51
Given Kudos: 56
Posts: 57
Kudos: 51
Let f(x) = x^2 + bx + c. If f(6) = 0 and f(-3) = 0, then b + c = 06 Jul 2019, 22:51
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

Tough and Tricky questions: Algebra.



Let f(x) = x^2 + bx + c. If f(6) = 0 and f(-3) = 0, then b + c =

A. 18
B. 15
C. -15
D. -21
E. -24

Kudos for a correct solution.



Sol : f(6) = 36 + 6b + c = 0
Or 6b+c = - 36 -- 1 )

F(-3) = 9 - 3B + C = 0
or , 3B - c = 9 -- 2)

Equating 1 & 2
B= -3 & C = -18

B+C = -3 +(-18) = -21
Moderator:
Bunuel
Math Expert
97815 posts