If f(x)=5x^2 and g(x)=x^2 + 12x + 85, what is the sum of all : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 24 Jan 2017, 03:18

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If f(x)=5x^2 and g(x)=x^2 + 12x + 85, what is the sum of all

Author Message
TAGS:

### Hide Tags

Director
Joined: 25 Oct 2008
Posts: 608
Location: Kolkata,India
Followers: 13

Kudos [?]: 799 [1] , given: 100

If f(x)=5x^2 and g(x)=x^2 + 12x + 85, what is the sum of all [#permalink]

### Show Tags

29 Oct 2009, 01:38
1
KUDOS
11
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

44% (03:40) correct 56% (02:22) wrong based on 54 sessions

### HideShow timer Statistics

If f(x)=5x^2 and g(x)=x^2 + 12x + 85, what is the sum of all values for k such that f (k+2)=g(2k)?

[Reveal] Spoiler:
Looks pretty simple..however I got stuck mid-way.
Got till $$K^2-4K-65=0$$
Does anyone know how to proceed further??

_________________

http://gmatclub.com/forum/countdown-beginshas-ended-85483-40.html#p649902

Last edited by Bunuel on 07 Oct 2012, 03:42, edited 1 time in total.
Renamed the topic and edited the question.
Senior Manager
Joined: 18 Aug 2009
Posts: 303
Followers: 3

Kudos [?]: 273 [0], given: 9

### Show Tags

29 Oct 2009, 02:11
Math Expert
Joined: 02 Sep 2009
Posts: 36625
Followers: 7103

Kudos [?]: 93617 [12] , given: 10583

### Show Tags

29 Oct 2009, 02:28
12
KUDOS
Expert's post
7
This post was
BOOKMARKED
tejal777 wrote:
$$If f(x)=5x^2 and g(x)=x^2 + 12x + 85$$, what is the sum of all values for k such that f (k+2)=g(2k) ?

Looks pretty simple..however I got stuck mid-way.
Got till $$K^2-4K-65=0$$
Does anyone know how to proceed further??

You've done everything right:

$$5*(k+2)^2=(2k)^2+12(2k)+85$$ --> $$k^2-4k-65=0$$.

Viete's formula for the roots $$x_1$$ and $$x_2$$ of equation $$ax^2+bx+c=0$$:

$$x_1+x_2=\frac{-b}{a}$$ AND $$x_1*x_2=\frac{c}{a}$$

So in our case the roots $$k_1+k_2=\frac{-(-4)}{1}=4$$
_________________
Senior Manager
Joined: 18 Aug 2009
Posts: 303
Followers: 3

Kudos [?]: 273 [1] , given: 9

### Show Tags

29 Oct 2009, 02:39
1
KUDOS
Bunuel wrote:
tejal777 wrote:
$$If f(x)=5x^2 and g(x)=x^2 + 12x + 85$$, what is the sum of all values for k such that f (k+2)=g(2k) ?

Looks pretty simple..however I got stuck mid-way.
Got till $$K^2-4K-65=0$$
Does anyone know how to proceed further??

You've done everything right:

$$5*(k+2)^2=(2k)^2+12(2k)+85$$ --> $$k^2-4k-65=0$$.

Viete's formula for the roots $$x1$$ and $$x2$$ of equation $$ax^2+bx+c=0$$:

$$x1+x2=\frac{-b}{a}$$ AND $$x1*x2=\frac{c}{a}$$

So in our case the roots $$k1+k2=\frac{-(-4)}{1}=4$$

Wow! math buster
don't have it in GMAT notes... added now, thnx and +1
Manager
Joined: 15 Sep 2009
Posts: 137
Followers: 1

Kudos [?]: 22 [0], given: 2

### Show Tags

29 Oct 2009, 03:36
after simplification,we get the quadratic eqn

k^2-4k-65= 0

sum of all values of k will be equal to the sum of the roots of the above q.eqn = -b/a = 4

I will go with 4
Intern
Affiliations: CA - India
Joined: 27 Oct 2009
Posts: 45
Location: India
Schools: ISB - Hyderabad, NSU - Singapore
Followers: 20

Kudos [?]: 695 [0], given: 5

### Show Tags

29 Oct 2009, 04:47
I tried solving this by quadratic equation formula and got 2 answers - 2+ or -\sqrt{65}.

What could be the other two possible values of k?
SVP
Joined: 16 Nov 2010
Posts: 1672
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 33

Kudos [?]: 514 [0], given: 36

### Show Tags

09 May 2011, 04:40
5(k+2)^2 = 4k^2 + 24k + 85

=> 5(k^2 + 4k + 4) = 4k^2 + 24k + 85

=> 5k^2 + 20k + 20 = 4k^2 + 24k + 85

=> k^2 - 4k - 65 = 0

No need to solve this, we need sum of two values of k:

So sum of roots = -b/a = -(-4) = 4
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

VP
Status: Current Student
Joined: 24 Aug 2010
Posts: 1345
Location: United States
GMAT 1: 710 Q48 V40
WE: Sales (Consumer Products)
Followers: 107

Kudos [?]: 420 [0], given: 73

### Show Tags

09 May 2011, 13:39
f(x)=5x^2
g(x)=x^2+12x+85
f(k+2)=5 (k+2)^2= 5(k^2+4k+4)=5k^2+20k+20

g(2k)= (2k)^2+ 12(2k)+85=4k^2+24k+85

5^k2+20k+20=4k^2+24k+85
k^2-4k-65=0

Using the quadratic equation (-b +/-\sqrt{b2-4ac}/2a we find the roots as follows

-(-4)+/-\sqrt{4^2 - 4(1)(-65)}/2(1)
So the first root is
4+\sqrt{16+260}/2 = 4+\sqrt{276}/2= 4+2\sqrt{69}/2
The second root is
4-\sqrt{16+260}/2 = 4-\sqrt{276}/2= 4-2\sqrt{69}/2

The sum of the roots is
4+2\sqrt{69}/2 + 4-2\sqrt{69}/2 = 8/2= 4
_________________

The Brain Dump - From Low GPA to Top MBA (Updated September 1, 2013) - A Few of My Favorite Things--> http://cheetarah1980.blogspot.com

Director
Joined: 01 Feb 2011
Posts: 755
Followers: 14

Kudos [?]: 115 [0], given: 42

### Show Tags

09 May 2011, 15:59
sum of two roots of a quadratic equation is -b/a

now we have $$k^2-4k-65$$

=> - b/a = 4
Manager
Status: Time to apply!
Joined: 24 Aug 2011
Posts: 220
Location: India
Concentration: Finance, Entrepreneurship
GMAT 1: 600 Q48 V25
GMAT 2: 660 Q50 V29
GMAT 3: 690 Q49 V34
GPA: 3.2
WE: Engineering (Computer Software)
Followers: 4

Kudos [?]: 113 [0], given: 166

### Show Tags

24 Nov 2011, 22:42
I also got 4
_________________

Didn't give up !!! Still Trying!!

Senior Manager
Joined: 06 Aug 2011
Posts: 405
Followers: 2

Kudos [?]: 193 [0], given: 82

### Show Tags

07 Oct 2012, 00:38
How do we get 4??

-b/a?? what is concept behind it??

k2-4k-65=0?? i cant solve after that..

_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

Math Expert
Joined: 02 Sep 2009
Posts: 36625
Followers: 7103

Kudos [?]: 93617 [1] , given: 10583

### Show Tags

07 Oct 2012, 03:48
1
KUDOS
Expert's post
2
This post was
BOOKMARKED
sanjoo wrote:
How do we get 4??

-b/a?? what is concept behind it??

k2-4k-65=0?? i cant solve after that..

It's called Viete's theorem, which 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 $$x_1*x_2=\frac{c}{a}$$.

Now, if we apply this to $$k^2-4k-65=0$$, we'll get that the sum of the roots must be $$k_1+k_2=\frac{-(-4)}{1}=4$$.

Hope it's clear.
_________________
Senior Manager
Joined: 06 Aug 2011
Posts: 405
Followers: 2

Kudos [?]: 193 [0], given: 82

Re: If f(x)=5x^2 and g(x)=x^2 + 12x + 85, what is the sum of all [#permalink]

### Show Tags

07 Oct 2012, 09:59
Thanks Alot BUNUEL..

i didnt see formula like this in my life new things very hard to digest ..
_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 25

Kudos [?]: 434 [0], given: 11

Re: If f(x)=5x^2 and g(x)=x^2 + 12x + 85, what is the sum of all [#permalink]

### Show Tags

10 Dec 2012, 04:13
$$f(k+2) = 5(k+2)^2 = 5(k^2 + 4k + 4) = 5k^2 + 20k + 20$$
$$g(2k) = 4k^2 + 24k + 85$$

$$5k^2 + 20k + 20 = 4k^2 + 24k + 85$$
$$k^2 - 4k -65 = 0$$

Trick: Sum of all roots: k1 + k2 = -b/a

$$k1 + k2 = - \frac{-4}{1} = 4$$

_________________

Impossible is nothing to God.

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13537
Followers: 577

Kudos [?]: 163 [0], given: 0

Re: If f(x)=5x^2 and g(x)=x^2 + 12x + 85, what is the sum of all [#permalink]

### Show Tags

10 Jan 2014, 13:57
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.
_________________
Current Student
Joined: 06 Sep 2013
Posts: 2035
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 62

Kudos [?]: 594 [0], given: 355

Re: If f(x)=5x^2 and g(x)=x^2 + 12x + 85, what is the sum of all [#permalink]

### Show Tags

23 Apr 2014, 05:57
Could we try posting some answer choices for this one?

I suggest the following

A) -4
B) 4
C) 65
D) -8
E) 8

Thanks!
Cheers
J
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13537
Followers: 577

Kudos [?]: 163 [0], given: 0

Re: If f(x)=5x^2 and g(x)=x^2 + 12x + 85, what is the sum of all [#permalink]

### Show Tags

13 Jan 2016, 09:16
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.
_________________
Re: If f(x)=5x^2 and g(x)=x^2 + 12x + 85, what is the sum of all   [#permalink] 13 Jan 2016, 09:16
Similar topics Replies Last post
Similar
Topics:
1 What is the sum of ALL the factors of 49? 5 16 Nov 2016, 03:53
6 What is the sum of odd integers from 35 to 85, inclusive? 2 03 Jul 2016, 10:27
If f(x)=3x−√x and g(x)=x^2, what is f(g(4))? 2 09 Dec 2015, 07:26
33 If f(x) = 5x^2 - 4 and g(x) = 3x + 1, then what is the sum 13 09 Jul 2014, 05:06
30 What is the sum of all remainders obtained when the first 17 12 Nov 2011, 15:45
Display posts from previous: Sort by