Find all School-related info fast with the new School-Specific MBA Forum

It is currently 22 Sep 2014, 10:45

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Find the value of 'a' and 'b' if sq root of 3 is a root of

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior Manager
User avatar
Joined: 30 Aug 2003
Posts: 330
Location: BACARDIVILLE
Followers: 1

Kudos [?]: 1 [0], given: 0

GMAT Tests User
Find the value of 'a' and 'b' if sq root of 3 is a root of [#permalink] New post 26 Jan 2004, 15:54
Find the value of 'a' and 'b' if sq root of 3 is a root of the equation
x^2 +ax - 6 = 0
and the equation x^2 +ax + b = 0 has real and equal roots.
_________________

Pls include reasoning along with all answer posts.
****GMAT Loco****
Este examen me conduce jodiendo loco

Manager
Manager
User avatar
Joined: 26 Dec 2003
Posts: 227
Location: India
Followers: 1

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

GMAT Tests User
 [#permalink] New post 26 Jan 2004, 16:13
a= sqrt 3 and b= 3/4, when the euation has real and equal roots then D=0 ie b^2-4ac=0, we know that b=a, a=1 and c=b then by substituting we get a^2-4b=0, ie a^2=4b-----------(1)


we are given that sum of roots= -a and product = -6 let x and y be the roots then x+y=-a and xy= -6 and also we are given that x= sqrt3 so by substituting we get a= sqrt 3 and by substituting this value in eq (1) above we get b= 3/4
Senior Manager
Senior Manager
User avatar
Joined: 30 Aug 2003
Posts: 330
Location: BACARDIVILLE
Followers: 1

Kudos [?]: 1 [0], given: 0

GMAT Tests User
 [#permalink] New post 26 Jan 2004, 16:26
Your answer is correct, but
why does c=b , and not c=-6?
_________________

Pls include reasoning along with all answer posts.
****GMAT Loco****
Este examen me conduce jodiendo loco

Manager
Manager
User avatar
Joined: 26 Dec 2003
Posts: 227
Location: India
Followers: 1

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

GMAT Tests User
 [#permalink] New post 26 Jan 2004, 16:35
in the first equation we r already given one root so we find out the other root and in the second equation its given that the roots are real and equal so D which is the discriminant= 0 and we know that D=b^2-4ac for a quad eq of the form ax^2 + bx +c =0
SVP
SVP
User avatar
Joined: 30 Oct 2003
Posts: 1798
Location: NewJersey USA
Followers: 4

Kudos [?]: 35 [0], given: 0

GMAT Tests User
 [#permalink] New post 29 Jan 2004, 12:40
a = sqrt(3)
and b >= 3/4
( if b = 3/4 ) then the second eq has real and equal roots
( if b > 3/4 ) then the eq has no equal and real roots

for first eq this is what I did

x^2+ax-6 = (x+sqrt(3) ) ( x+k )

x^2+x(k-sqrt(3))-k*sqrt(3) = x^2+ax-6
so k*sqrt(3) = 6 hence k = 2*sqrt(3)
so a = sqrt(3)
substitute value of a in second equation and find the roots
  [#permalink] 29 Jan 2004, 12:40
    Similar topics Author Replies Last post
Similar
Topics:
sq root fivedaysleft 3 05 Jul 2011, 21:56
One root; Find the value of k petrifiedbutstanding 3 17 Apr 2011, 08:17
What is the value of x? sq root(x^4)=9 sq root(x^2)=-x tejal777 7 06 Nov 2009, 05:32
1 Sq. Root reply2spg 2 28 Oct 2009, 15:12
multiplying sq roots bmwhype2 2 30 Dec 2007, 15:04
Display posts from previous: Sort by

Find the value of 'a' and 'b' if sq root of 3 is a root of

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.