BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

squares of their reciprocals

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

squares of their reciprocals

by sanju09 » Wed Mar 03, 2010 2:38 am
If the sum of the roots of the equation x^2 + t x + 1 = 0 is equal to the sum of the squares of their reciprocals, then which of the following is a possible value of t?
(A) -1
(B) 0
(C) ½
(D) 1
(E) 2
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1132
Joined: Mon Jul 20, 2009 3:38 am
Location: India
Thanked: 64 times
Followed by:6 members
GMAT Score:760

by harsh.champ » Wed Mar 03, 2010 4:14 am
sanju09 wrote:If the sum of the roots of the equation x^2 + t x + 1 = 0 is equal to the sum of the squares of their reciprocals, then which of the following is a possible value of t?
(A) -1
(B) 0
(C) ½
(D) 1
(E) 2
Let the roots be a and b.
a+b=-t
ab = 1
Sum of squares of their reciprocals = 1/a^2 + 1/ b^2
=(a^2 + b^2)/(ab)^2
=[(a+b)^2 - 2ab]/(ab)^2
= t^2 - 2
Now, t^2 - 2 = -t
=>t^2 +t - 2 = 0
[spoiler]t= 1 D[/spoiler]
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

"Keep Walking" - Johnny Walker :P
Top
Post new topic Post Reply
• Page 1 of 1