Author 
Message 
TAGS:

Hide Tags

Director
Joined: 25 Oct 2008
Posts: 516
Location: Kolkata,India

If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value
[#permalink]
Show Tags
Updated on: 04 Mar 2018, 07:33
Question Stats:
58% (02:35) correct 42% (03:08) wrong based on 103 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)? A. 8 B. 4 C. 4 D. 8 E. 65 Looks pretty simple..however I got stuck midway. Got till \(K^24K65=0\) Does anyone know how to proceed further??
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
http://gmatclub.com/forum/countdownbeginshasended8548340.html#p649902
Originally posted by tejal777 on 29 Oct 2009, 02:38.
Last edited by Bunuel on 04 Mar 2018, 07:33, edited 2 times in total.
Renamed the topic and edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 50007

If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value
[#permalink]
Show Tags
29 Oct 2009, 03:28




Senior Manager
Joined: 18 Aug 2009
Posts: 284

Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value
[#permalink]
Show Tags
29 Oct 2009, 03:39
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 midway. Got till \(K^24K65=0\) Does anyone know how to proceed further?? You've done everything right: \(5*(k+2)^2=(2k)^2+12(2k)+85\) > \(k^24k65=0\). 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: 117

Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value
[#permalink]
Show Tags
29 Oct 2009, 04:36
after simplification,we get the quadratic eqn
k^24k65= 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: 43
Location: India
Schools: ISB  Hyderabad, NSU  Singapore

Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value
[#permalink]
Show Tags
29 Oct 2009, 05:47
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?



Retired Moderator
Joined: 16 Nov 2010
Posts: 1436
Location: United States (IN)
Concentration: Strategy, Technology

Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value
[#permalink]
Show Tags
09 May 2011, 05:40
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: 1338
Location: United States
WE: Sales (Consumer Products)

Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value
[#permalink]
Show Tags
09 May 2011, 14:39
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^24k65=0 Using the quadratic equation (b +/\sqrt{b24ac}/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= 42\sqrt{69}/2 The sum of the roots is 4+2\sqrt{69}/2 + 42\sqrt{69}/2 = 8/2= 4 The answer should be 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: 668

Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value
[#permalink]
Show Tags
09 May 2011, 16:59
sum of two roots of a quadratic equation is b/a
now we have \(k^24k65\)
=>  b/a = 4



Senior Manager
Joined: 06 Aug 2011
Posts: 341

Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value
[#permalink]
Show Tags
07 Oct 2012, 01:38
How do we get 4?? b/a?? what is concept behind it?? k24k65=0?? i cant solve after that.. plz do explain..Thanks in advance
_________________
Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !



Math Expert
Joined: 02 Sep 2009
Posts: 50007

Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value
[#permalink]
Show Tags
07 Oct 2012, 04:48



Senior Manager
Joined: 06 Aug 2011
Posts: 341

Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value
[#permalink]
Show Tags
07 Oct 2012, 10:59
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: 431
Concentration: Marketing, Finance
GPA: 3.23

Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value
[#permalink]
Show Tags
10 Dec 2012, 05:13
\(f(k+2) = 5(k+2)^2 = 5(k^2 + 4k + 4) = 5k^2 + 20k + 20\) \(g(2k) = 4k^2 + 24k + 85\) \(5k^2 + 20k + 20 = 4k^2 + 24k + 85\) \(k^2  4k 65 = 0\) Trick: Sum of all roots: k1 + k2 = b/a \(k1 + k2 =  \frac{4}{1} = 4\) Answer: 4
_________________
Impossible is nothing to God.



Manager
Joined: 26 Feb 2018
Posts: 59
WE: Sales (Internet and New Media)

Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value
[#permalink]
Show Tags
04 Mar 2018, 07:25
Bunuel , Can we have more this kinda questions of functions ?
_________________
" Can't stop learning and failing"



Math Expert
Joined: 02 Sep 2009
Posts: 50007

Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value
[#permalink]
Show Tags
04 Mar 2018, 07:35



Manager
Joined: 26 Feb 2018
Posts: 59
WE: Sales (Internet and New Media)

Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value
[#permalink]
Show Tags
04 Mar 2018, 07:46
Thanks a lot Bunuel !
_________________
" Can't stop learning and failing"




Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value &nbs
[#permalink]
04 Mar 2018, 07:46






