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# Is A positive? 1. x^2-2*x+A is positive for all x 2. A*x^2+1

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Manager
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Is A positive? 1. x^2-2*x+A is positive for all x 2. A*x^2+1 [#permalink]  02 Apr 2005, 08:39
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Is A positive?
1. x^2-2*x+A is positive for all x
2. A*x^2+1 is positive for all x
VP
Joined: 18 Nov 2004
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[#permalink]  02 Apr 2005, 09:41
"E"

state 1...A > 2x-x^2....insuff to tell if A > 0

state 2....Ax^2 + 1 > 0

A > -1/x^2...........as x^2 is always positive...A can be -ve or +ve

combine

(A+1)x^2 -2x + (A+1) > 0

A > (2x - x^2 -1)/x^2+1...still insuff
Director
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[#permalink]  02 Apr 2005, 10:49
Why not B?

state 2....Ax^2 + 1 > 0

==>> A > -1/(x^2)

whatever the value of x is, A is always negative....unless x is a complex number of form x=y+iz where i^2 = -1
VP
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[#permalink]  02 Apr 2005, 11:25
gmat2me2 wrote:
Why not B?

state 2....Ax^2 + 1 > 0

==>> A > -1/(x^2)

whatever the value of x is, A is always negative....unless x is a complex number of form x=y+iz where i^2 = -1

A is not always -ve e.g....if A > -1...doesn't mean A is always -ve....A can be 3 or A can be -0.5
Director
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[#permalink]  02 Apr 2005, 14:32
banerjeea_98 wrote:
gmat2me2 wrote:
Why not B?

state 2....Ax^2 + 1 > 0

==>> A > -1/(x^2)

whatever the value of x is, A is always negative....unless x is a complex number of form x=y+iz where i^2 = -1

A is not always -ve e.g....if A > -1...doesn't mean A is always -ve....A can be 3 or A can be -0.5

But that depends on the value of x^2 which is +ve for any value , right?

What I think is how can we get a vlue for the above eq which returns a +ve value and assign to A?
VP
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[#permalink]  02 Apr 2005, 16:24
Yes, ur RHS is always -ve, but just by saying that
A > (some -ve number) doesn't mean that A is ALWAYS
+ve or -ve.....i.e. if A > -1....can u tell if A is always +ve or -ve ?....only when u have A > 0, u can tell that A is +ve for sure.
Director
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[#permalink]  02 Apr 2005, 17:39
banerjeea_98 wrote:
Yes, ur RHS is always -ve, but just by saying that
A > (some -ve number) doesn't mean that A is ALWAYS
+ve or -ve.....i.e. if A > -1....can u tell if A is always +ve or -ve ?....only when u have A > 0, u can tell that A is +ve for sure.

Agreed...Thanks though for a good explanation
Manager
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[#permalink]  04 Apr 2005, 07:13
OA is A.
I got this one wrong with E as well.

OE is:
St1. can be rewritten as (x-1)^2 + A-1>0, for this to hold true for all possible values of x, A > 1. So sufficient.
SVP
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Re: DS - Is A +ve? [#permalink]  04 Apr 2005, 07:50
1. x^2-2*x+A >0
A>-(x-1)^2+1>=1>0
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VP
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[#permalink]  04 Apr 2005, 08:29
hmmm...let's consider x = 3 for state 1

9-6+A > 0

3+A > 0

to keep the LHS > 0....we can put A = -2 or A = 2....in one case A > 0 and in other A < 0 ....or is it becose it has to satify for ALL values of x
[#permalink] 04 Apr 2005, 08:29
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# Is A positive? 1. x^2-2*x+A is positive for all x 2. A*x^2+1

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