equal in magnitude but opposite in sign

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 am; Location: India; Thanked: 267 times; Followed by:80 members; GMAT Score:760

equal in magnitude but opposite in sign

by sanju09 » Sat Jul 31, 2010 5:53 am

Which of the following equations has roots that are equal in magnitude but opposite in sign to the roots of the equation x^2 + 5 x + 6 = 0?
A. x^2 + 6 x - 5 = 0
B. x^2 + 5 x - 6 = 0
C. x^2 + 6 x + 5 = 0
D. x^2 - 5 x + 6 = 0
E. x^2 - 5 x - 6 = 0

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Source: Beat The GMAT — Problem Solving | Sat Jul 31, 2010 5:53 am

outreach: Legendary Member; Posts: 748; Joined: Sun Jan 31, 2010 7:54 am; Thanked: 46 times; Followed by:3 members

by outreach » Sat Jul 31, 2010 8:12 am

roots of x^2 + 5 x + 6 = 0 are -2 and -3
D
roots of x^2 - 5 x + 6 = 0 are 2 and 3

sanju09 wrote:Which of the following equations has roots that are equal in magnitude but opposite in sign to the roots of the equation x^2 + 5 x + 6 = 0?
A. x^2 + 6 x - 5 = 0
B. x^2 + 5 x - 6 = 0
C. x^2 + 6 x + 5 = 0
D. x^2 - 5 x + 6 = 0
E. x^2 - 5 x - 6 = 0

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by Brent@GMATPrepNow » Sat Jul 31, 2010 8:13 am

sanju09 wrote:Which of the following equations has roots that are equal in magnitude but opposite in sign to the roots of the equation x^2 + 5 x + 6 = 0?
A. x^2 + 6 x - 5 = 0
B. x^2 + 5 x - 6 = 0
C. x^2 + 6 x + 5 = 0
D. x^2 - 5 x + 6 = 0
E. x^2 - 5 x - 6 = 0
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First we'll solve x^2 + 5 x + 6 = 0 by factoring the left hand side.
(x+2)(x+3)=0 --> x= -2 and = -3

So, we want a new equation such that the roots are 2 and 3
Well the equation (x-2)(x-3)=0 will have roots 2 and 3
When we expand we get x^2 - 5x + 6 = 0
Answer=D

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