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cannot lie between

by sanju09 » Thu Oct 14, 2010 2:49 am
Value of the expression (x^2 - x + 1)/ (x - 1) cannot lie between
(A) -1, -3
(B) 1, -3
(C) -1, 2
(D) -1, 3
(E) 1, 3


[spoiler]Made up[/spoiler]
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by fskilnik@GMATH » Thu Oct 14, 2010 4:27 am
sanju09 wrote:Value of the expression (x^2 - x + 1)/ (x - 1) cannot lie between
(A) -1, -3
(B) 1, -3
(C) -1, 2
(D) -1, 3
(E) 1, 3
Nice idea, sanju09!

I will give my shot, ok?

Answer: D

Let the expression given be equal to m, where m is a fixed real number. It is easy to come to the following 2o degree equation in the (real) variable x:

x^2 - x(1+m)+(1+m) = 0

Calculating the discriminant and imposing it NEGATIVE, we will get m^2 - 2m - 3 < 0, then we have -1 < m < 3.

Interpretation: for values of m between -1 and 3, there are no real numbers x such that the expression is equal to m.

That´s what you had in mind?

Best Regards,
Fábio.
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by shovan85 » Thu Oct 14, 2010 4:32 am
sanju09 wrote:Value of the expression (x^2 - x + 1)/ (x - 1) cannot lie between
(A) -1, -3
(B) 1, -3
(C) -1, 2
(D) -1, 3
(E) 1, 3


[spoiler]Made up[/spoiler]
IMO D.

Just tried some value by taking x=0,1,-1,-1/2
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by sanju09 » Thu Oct 14, 2010 4:55 am
fskilnik wrote:
sanju09 wrote:Value of the expression (x^2 - x + 1)/ (x - 1) cannot lie between
(A) -1, -3
(B) 1, -3
(C) -1, 2
(D) -1, 3
(E) 1, 3
Nice idea, sanju09!

I will give my shot, ok?

Answer: D

Let the expression given be equal to m, where m is a fixed real number. It is easy to come to the following 2o degree equation in the (real) variable x:

x^2 - x(1+m)+(1+m) = 0

Calculating the discriminant and imposing it NEGATIVE, we will get m^2 - 2m - 3 < 0, then we have -1 < m < 3.

Interpretation: for values of m between -1 and 3, there are no real numbers x such that the expression is equal to m.

That´s what you had in mind?

Best Regards,
Fábio.
hmmm...so you read minds too!! Well, you certainly deserve an on records 'THANKS' from me. Nice job, sir
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
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by fskilnik@GMATH » Thu Oct 14, 2010 4:59 am
Thanks! :)
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