Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47946

If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
[#permalink]
Show Tags
09 Jul 2014, 06:06
Question Stats:
65% (02:04) correct 35% (02:33) wrong based on 385 sessions
HideShow timer Statistics




Math Expert
Joined: 02 Sep 2009
Posts: 47946

Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
[#permalink]
Show Tags
09 Jul 2014, 06:06




Intern
Joined: 24 Apr 2013
Posts: 16
Location: Russian Federation

Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
[#permalink]
Show Tags
09 Jul 2014, 08:46
F(x)=5x^24 F(m1)=5(m1)^24 5(m^22m+1)4 5m^210m+54 5m^210m+1
G(x)=3x+1 G(m^2+1)=3(m^2+1)+1 3m^2+3+1 3m^2+4
5m^210m+1=3m^2+4 2m^210m3=0
D=b^24ac D=1004(6)=100+24=124
x(1) = 10+2(root)31/4 x(2) = 102(root)31/4
10+2(root)31/4 + 102(root)31/4 = 20/4 = 5
Answer is D



Intern
Joined: 19 Nov 2013
Posts: 25
Location: India
Concentration: Strategy, Technology
WE: Information Technology (Computer Software)

Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
[#permalink]
Show Tags
09 Jul 2014, 08:53
The ans is 5
putting the values gives us 2m^210m3=0
solving this gives us m= (10+sqrt(124))/4 and (10sqrt(124))/4
21/41/4 =5 ans



Senior Manager
Joined: 13 Jun 2013
Posts: 277

Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
[#permalink]
Show Tags
09 Jul 2014, 10:19
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(m1)= 5(m1)^2 4 = 5(m^2+12m) 4 =5m^2+510m4 = 5m^210m +1 g(m^2+1)= 3(m^2+1) +1 =3m^2+4 now f(m1)=g(m^2+1) 5m^210m +1 = 3m^2+4 2m^210m 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^25m3/2=0 thus sum of roots = 5 hence D



Intern
Joined: 29 Oct 2013
Posts: 18

Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
[#permalink]
Show Tags
09 Jul 2014, 12:11
Substituting (m1) and (m^2+1) in place of x in the functions f(x) and g(x) respectively,
5(m1)^24=3(m^2+1) 5m^210m+54=3m^2+3+1 2m^210m=0 2m(m5)=0
2m=0 and m5=0
The roots of m are 0 and 5 and their sum is 5
Answer D



Intern
Joined: 23 May 2014
Posts: 10

Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
[#permalink]
Show Tags
09 Jul 2014, 18:33
Subbing (m1) into f(x) yields 5m^2  10m + 1
Subbing (m^2 + 1) into g(x) yields 3m^2 + 4
Setting f(m1) 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.



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1835
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
[#permalink]
Show Tags
09 Jul 2014, 22:42
\(f(x) = 5x^2  4\) \(f(m1) = 5 (m1)^2  4\) \(= 5(m^2  2m + 1)  4\) \(= 5m^2  10m + 5  4\) \(= 5m^2  10m + 1\) .............. (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
_________________
Kindly press "+1 Kudos" to appreciate



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1835
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
[#permalink]
Show Tags
09 Jul 2014, 22:46
fra wrote: Substituting (m1) and (m^2+1) in place of x in the functions f(x) and g(x) respectively,
5(m1)^24=3(m^2+1) 5m^210m+54=3m^2+3+1 2m^210m=0 2m(m5)=0
2m=0 and m5=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
_________________
Kindly press "+1 Kudos" to appreciate



Intern
Joined: 29 Oct 2013
Posts: 18

Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
[#permalink]
Show Tags
10 Jul 2014, 00:37
Thanks for pointing that out!



Math Expert
Joined: 02 Sep 2009
Posts: 47946

Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
[#permalink]
Show Tags
15 Jul 2014, 10:31



Current Student
Joined: 29 Mar 2015
Posts: 77
Concentration: Strategy, Operations
WE: Research (Other)

Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
[#permalink]
Show Tags
17 Apr 2015, 05:21
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(m1) = g(m^2+1) 5(m1)^24=3(m^2+1)+1 2m^2  10m  3 = 0 Sum of roots is = b/a so 10/2 = 5
_________________
If you like my post, Pl. do not hesitate to press kudos!!!!
Q51 on GMAT  PM me if you need any help with GMAT QUANTS!!!



Intern
Joined: 10 May 2016
Posts: 9

Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
[#permalink]
Show Tags
11 May 2016, 02:47
f(m1) = g(m^2+1) 5(m1)^24=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



SVP
Joined: 08 Jul 2010
Posts: 2138
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
[#permalink]
Show Tags
09 Apr 2017, 02:05
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. 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 [ 2.91 MiB  Viewed 7098 times ]
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



SVP
Joined: 26 Mar 2013
Posts: 1778

Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
[#permalink]
Show Tags
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



SVP
Joined: 08 Jul 2010
Posts: 2138
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
[#permalink]
Show Tags
10 Apr 2017, 03:18
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.
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



NonHuman User
Joined: 09 Sep 2013
Posts: 7733

Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum
[#permalink]
Show Tags
25 Jul 2018, 21:28
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 Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If f(x) = 5x^2  4 and g(x) = 3x + 1, then what is the sum &nbs
[#permalink]
25 Jul 2018, 21:28






