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

 It is currently 30 Mar 2015, 08:16

### 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

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

Author Message
TAGS:
Senior Manager
Joined: 30 Aug 2003
Posts: 330
Location: BACARDIVILLE
Followers: 1

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

Find the value of 'a' and 'b' if sq root of 3 is a root of [#permalink]  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
Joined: 26 Dec 2003
Posts: 227
Location: India
Followers: 1

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

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
Joined: 30 Aug 2003
Posts: 330
Location: BACARDIVILLE
Followers: 1

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

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
Joined: 26 Dec 2003
Posts: 227
Location: India
Followers: 1

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

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
Joined: 30 Oct 2003
Posts: 1797
Location: NewJersey USA
Followers: 5

Kudos [?]: 41 [0], given: 0

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
Similar topics Replies Last post
Similar
Topics:
sq root 3 05 Jul 2011, 21:56
One root; Find the value of k 3 17 Apr 2011, 08:17
What is the value of x? sq root(x^4)=9 sq root(x^2)=-x 7 06 Nov 2009, 05:32
1 Sq. Root 2 28 Oct 2009, 15:12
multiplying sq roots 2 30 Dec 2007, 15:04
Display posts from previous: Sort by