NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 16:31 It is currently 24 Apr 2024, 16:31
Decision Tracker
My Rewards
New posts
New comers' posts

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

If f(x) = 5x^2 - 4 and g(x) = 3x + 1, then what is the sum

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618811 [66]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
If f(x) = 5x^2 - 4 and g(x) = 3x + 1, then what is the sum [#permalink] New post   09 Jul 2014, 06:06
9
Kudos
57
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

66% (02:33) correct 34% (02:56) wrong based on 848 sessions
Hide Show timer Statistics


If \(f(x) = 5x^2 - 4\) and \(g(x) = 3x + 1\), then what is the sum of all the values of \(m\) for which \(f(m - 1) = g(m^2 + 1)\) ?

A. -10
B. -5
C. 0
D. 5
E. 10

Kudos for a correct solution.



Experience a GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
GMAT Club Tests Check Our Products Try Free Tests
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618811 [37]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Re: If f(x) = 5x^2 - 4 and g(x) = 3x + 1, then what is the sum [#permalink] New post   09 Jul 2014, 06:06
13
Kudos
24
Bookmarks
Expert Reply
SOLUTION

If \(f(x) = 5x^2 - 4\) and \(g(x) = 3x + 1\), then what is the sum of all the values of \(m\) for which \(f(m - 1) = g(m^2 + 1)\) ?

A. -10
B. -5
C. 0
D. 5
E. 10

\(f(x) = 5x^2 - 4\), then \(f(m - 1)=5(m-1)^2 - 4=5m^2-10 m+1\);
\(g(x) = 3x + 1\), then \(g(m^2 + 1)=3(m^2 + 1) + 1=3m^2+4\).

Since given that \(f(m - 1) = g(m^2 + 1)\), then \(5m^2-10 m+1=3m^2+4\) --> \(2m^2-10m-3=0\).

Next, 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 \(x_1*x_2=\frac{c}{a}\).

Thus according to the above \(m_1+m_2=\frac{-(-10)}{2}=5\).

Answer: D.

Try NEW Algebra DS question.
General Discussion
User avatar
manpreetsingh86
Manager
Manager
Joined: 13 Jun 2013
Posts: 223
Own Kudos [?]: 1046 [3]
Given Kudos: 14
Send PM
Re: If f(x) = 5x^2 - 4 and g(x) = 3x + 1, then what is the sum [#permalink] New post   09 Jul 2014, 10:19
3
Kudos
Bunuel wrote:


If \(f(x) = 5x^2 - 4\)and \(g(x) = 3x + 1\), then what is the sum of all the values of \(m\) for which \(f(m - 1) = g(m^2 + 1)\) ?

A. -10
B. -5
C. 0
D. 5
E. 10

Kudos for a correct solution.



f(m-1)= 5(m-1)^2 -4
= 5(m^2+1-2m) -4
=5m^2+5-10m-4
= 5m^2-10m +1

g(m^2+1)= 3(m^2+1) +1
=3m^2+4

now f(m-1)=g(m^2+1)
5m^2-10m +1 = 3m^2+4
2m^2-10m -3=0

also, any quadratic equation can be written as
x^2-(sum of the roots)x + product of the roots

here since coeff. of m^2 is 2, therefore we will divide the whole expression by 2
and we will get, m^2-5m-3/2=0

thus sum of roots = 5

hence D
avatar
PareshGmat
SVP
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1562
Own Kudos [?]: 7208 [3]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Send PM
Re: If f(x) = 5x^2 - 4 and g(x) = 3x + 1, then what is the sum [#permalink] New post   09 Jul 2014, 22:42
2
Kudos
1
Bookmarks
\(f(x) = 5x^2 - 4\)

\(f(m-1) = 5 (m-1)^2 - 4\)

\(= 5(m^2 - 2m + 1) - 4\)

\(= 5m^2 - 10m + 5 - 4\)

\(= 5m^2 - 10m + 1\) .............. (1)

g(x) = 3x+1

\(g(m^2 + 1) = 3(m^2 + 1) + 1\)

\(= 3m^2 + 4\) ............ (2)

Equating (1) & (2)

\(5m^2 - 10m + 1 = 3m^2 + 4\)

\(2m^2 - 10m - 3 = 0\)

Sum of roots \(= \frac{-(-10)}{2} = 5\)

Answer = D
User avatar
S
VladimirKarpov
Intern
Intern
Joined: 24 Apr 2013
Posts: 12
Own Kudos [?]: 38 [2]
Given Kudos: 18
Location: Russian Federation
Send PM
GMAT ToolKit User
Re: If f(x) = 5x^2 - 4 and g(x) = 3x + 1, then what is the sum [#permalink] New post   09 Jul 2014, 08:46
2
Kudos
F(x)=5x^2-4
F(m-1)=5(m-1)^2-4
5(m^2-2m+1)-4
5m^2-10m+5-4
5m^2-10m+1

G(x)=3x+1
G(m^2+1)=3(m^2+1)+1
3m^2+3+1
3m^2+4

5m^2-10m+1=3m^2+4
2m^2-10m-3=0

D=b^2-4ac
D=100-4(-6)=100+24=124

x(1) = 10+2(root)31/4
x(2) = 10-2(root)31/4

10+2(root)31/4 + 10-2(root)31/4 = 20/4 = 5

Answer is D
User avatar
M3sSiaH
Manager
Manager
Joined: 29 Mar 2015
Posts: 69
Own Kudos [?]: 45 [2]
Given Kudos: 21
Concentration: Strategy, Operations
Schools: Kenan-Flagler '18 (I) NUS '18 (I) Olin '18 (I) Leipzig FT"18 (A) Mason '18 (A$) Rotman '18 (D)
GMAT 1: 700 Q51 V33
WE:Research (Other)
Send PM
GMAT ToolKit User Reviews Badge
Re: If f(x) = 5x^2 - 4 and g(x) = 3x + 1, then what is the sum [#permalink] New post   17 Apr 2015, 05:21
2
Kudos
If \(f(x) = 5x^2 - 4\) and \(g(x) = 3x + 1\), then what is the sum of all the values of \(m\) for which \(f(m - 1) = g(m^2 + 1)\) ?

A. -10
B. -5
C. 0
D. 5
E. 10

Kudos for a correct solution.

[/quote]

f(m-1) = g(m^2+1)
5(m-1)^2-4=3(m^2+1)+1
2m^2 - 10m - 3 = 0
Sum of roots is = -b/a
so 10/2 = 5
User avatar
manish2014
Intern
Intern
Joined: 19 Nov 2013
Posts: 22
Own Kudos [?]: 80 [1]
Given Kudos: 19
Location: India
Concentration: Strategy, Technology
WE:Information Technology (Computer Software)
Send PM
Re: If f(x) = 5x^2 - 4 and g(x) = 3x + 1, then what is the sum [#permalink] New post   09 Jul 2014, 08:53
1
Kudos
The ans is 5

putting the values gives us 2m^2-10m-3=0

solving this gives us m= (10+sqrt(124))/4 and (10-sqrt(124))/4

21/4-1/4 =5 ans
User avatar
fra
Intern
Intern
Joined: 29 Oct 2013
Posts: 16
Own Kudos [?]: 49 [1]
Given Kudos: 12
Send PM
Re: If f(x) = 5x^2 - 4 and g(x) = 3x + 1, then what is the sum [#permalink] New post   09 Jul 2014, 12:11
1
Kudos
Substituting (m-1) and (m^2+1) in place of x in the functions f(x) and g(x) respectively,

5(m-1)^2-4=3(m^2+1)
5m^2-10m+5-4=3m^2+3+1
2m^2-10m=0
2m(m-5)=0

2m=0 and m-5=0

The roots of m are 0 and 5 and their sum is 5

Answer D
User avatar
dbaremberg
Intern
Intern
Joined: 23 May 2014
Posts: 8
Own Kudos [?]: 7 [1]
Given Kudos: 11
Send PM
Re: If f(x) = 5x^2 - 4 and g(x) = 3x + 1, then what is the sum [#permalink] New post   09 Jul 2014, 18:33
1
Kudos
Subbing (m-1) into f(x) yields 5m^2 - 10m + 1

Subbing (m^2 + 1) into g(x) yields 3m^2 + 4

Setting f(m-1) equal to g(m^2 + 1) yields
3m^2 + 1 = 5m^2 - 10m + 1

This simplifies to
0 = 2m^2 - 10m - 3

Using Viete's rules, we know that the sum of the roots x1 and x2 in ax^2 + bx + c is equal to -b/a, hence
x1 + x2 = -(-10)/2 = 5

This is the desired answer. Therefore, D.
avatar
PareshGmat
SVP
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1562
Own Kudos [?]: 7208 [1]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Send PM
Re: If f(x) = 5x^2 - 4 and g(x) = 3x + 1, then what is the sum [#permalink] New post   09 Jul 2014, 22:46
1
Kudos
fra wrote:
Substituting (m-1) and (m^2+1) in place of x in the functions f(x) and g(x) respectively,

5(m-1)^2-4=3(m^2+1)
5m^2-10m+5-4=3m^2+3+1
2m^2-10m=0
2m(m-5)=0

2m=0 and m-5=0

The roots of m are 0 and 5 and their sum is 5

Answer D


Equation would come up as \(2m^2 - 10m - 3\)

Answer = D, however individual roots cannot be 0 & 5
User avatar
fra
Intern
Intern
Joined: 29 Oct 2013
Posts: 16
Own Kudos [?]: 49 [0]
Given Kudos: 12
Send PM
Re: If f(x) = 5x^2 - 4 and g(x) = 3x + 1, then what is the sum [#permalink] New post   10 Jul 2014, 00:37
Thanks for pointing that out!
avatar
UttamGiet
Intern
Intern
Joined: 10 May 2016
Posts: 7
Own Kudos [?]: 4 [0]
Given Kudos: 15
Send PM
Re: If f(x) = 5x^2 - 4 and g(x) = 3x + 1, then what is the sum [#permalink] New post   11 May 2016, 02:47
f(m-1) = g(m^2+1)
5(m-1)^2-4=3(m^2+1)+1
2m^2 - 10m - 3 = 0
For equation aX^2+bX+C=0 sum of roots =(-b/a)

so here sum of roots= -(-10/2) = 5
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5957
Own Kudos [?]: 13387 [0]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
Re: If f(x) = 5x^2 - 4 and g(x) = 3x + 1, then what is the sum [#permalink] New post   09 Apr 2017, 02:05
Expert Reply
Bunuel wrote:

New project from GMAT Club: Topic-wise questions with tips and hints!



If \(f(x) = 5x^2 - 4\) and \(g(x) = 3x + 1\), then what is the sum of all the values of \(m\) for which \(f(m - 1) = g(m^2 + 1)\) ?

A. -10
B. -5
C. 0
D. 5
E. 10

Kudos for a correct solution.



Pleas find attached the solution.

My opinion: it's highly unlikely to see a question based on these concepts in actual GMAT exam.

Posted from my mobile device
Attachments

File comment: GMATINSIGHT
1491728677848164508652.jpg
1491728677848164508652.jpg [ 2.91 MiB | Viewed 21651 times ]

User avatar
L
Mo2men
RSM Erasmus Moderator
Joined: 26 Mar 2013
Posts: 2461
Own Kudos [?]: 1360 [0]
Given Kudos: 641
Concentration: Operations, Strategy
Schools: Erasmus (II)
Send PM
Reviews Badge
Re: If f(x) = 5x^2 - 4 and g(x) = 3x + 1, then what is the sum [#permalink] New post   10 Apr 2017, 02:11
GMATinsight wrote:

Pleas find attached the solution.

My opinion: it's highly unlikely to see a question based on these concepts in actual GMAT exam.



Dear GMATInsight,

I'd like to draw you attention that there is an error in f(x) function. You have changed it from (-4) to (+4). The final quadratic equation should be:

2m^2 - 10m - 3 = 0
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5957
Own Kudos [?]: 13387 [0]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
Re: If f(x) = 5x^2 - 4 and g(x) = 3x + 1, then what is the sum [#permalink] New post   10 Apr 2017, 03:18
Expert Reply
Mo2men wrote:
GMATinsight wrote:

Pleas find attached the solution.

My opinion: it's highly unlikely to see a question based on these concepts in actual GMAT exam.



Dear GMATInsight,

I'd like to draw you attention that there is an error in f(x) function. You have changed it from (-4) to (+4). The final quadratic equation should be:

2m^2 - 10m - 3 = 0


Thanks for notifying my mistake... However the pleasant surprise is that answer still doesn't change as the answer is dependent on the coefficients of x^2 and x...

So I hope that is ok if I accept the mistake made in first step however endorse the method to find answer (roots) of a quadratic equation. :)
User avatar
S
GmatPoint
Senior Manager
Senior Manager
Joined: 02 Jan 2022
Posts: 266
Own Kudos [?]: 94 [0]
Given Kudos: 3
GMAT 1: 760 Q50 V42
Send PM
Re: If f(x) = 5x^2 - 4 and g(x) = 3x + 1, then what is the sum [#permalink] New post   03 Feb 2022, 03:38
Given \(f\left(x\right)\ =\ 5x^2-4 \) \(g\left(x\right)\ =\ 3x+1\)
Substituting the function for
\(f\left(m-1\right)\ =\ 5\left(m-1\right)^2-4\) = \(5\left(m^2-2m+1\right)-4\)
= \(5m^2-10m+1\)
Similarly for \(g\left(m^2+1\right)\)
= \(3\left(m^2+1\right)+1\)
Equating the two we have
\(2m^2-10m-3\ =\ 0\)
The sum of possible values of m is equal to the sum of roots of the equation which is equal to 5.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32655
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: If f(x) = 5x^2 - 4 and g(x) = 3x + 1, then what is the sum [#permalink] New post   17 Mar 2024, 23:11
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.
GMAT Club Bot
gmatclubot
Re: If f(x) = 5x^2 - 4 and g(x) = 3x + 1, then what is the sum [#permalink]
17 Mar 2024, 23:11
Moderators:
Bunuel
Math Expert
92900 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions