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Number properties I question #2

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Joined: 08 Nov 2009
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Location: United States
Concentration: Strategy, Sustainability
WE: Supply Chain Management (Hospitality and Tourism)
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Number properties I question #2 [#permalink] New post 27 Nov 2009, 13:43
I tried looking for an explanation for this before posting but hand no luck. If some one could point me to a thread that would be great!

Is A positive?

1. x^2 - 2x + A is positive for all x
2. Ax^2 + 1 is positive for all x

My question is is on statement 1, if x=-1 wouldnt it be possible for A to be negative? -1^2 + -2*(-1) + A = 1+2+A =3+A. Therfore A could be -2 and the statement would still be positive.

What am i missing here?

Thanks,
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Re: Number properties I question #2 [#permalink] New post 28 Nov 2009, 01:45
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1. x^2 - 2x + A is positive for all x

When x=0, x^2 - 2x + A=A. According to Statement1 it should be positive, soA>0, SUFF

2.Ax^2 + 1 is positive for all x

Ax^2 + 1>0
Ax^2>-1

Here x^2 is always positive, but A could be both positive OR negative. Consider x=1/3, A=-1; Ax^2=-1/9>-1

INSUFF

Answer: (A)
Current Student
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Joined: 08 Nov 2009
Posts: 59
Location: United States
Concentration: Strategy, Sustainability
WE: Supply Chain Management (Hospitality and Tourism)
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Kudos [?]: 8 [0], given: 3

Re: Number properties I question #2 [#permalink] New post 28 Nov 2009, 06:53
Thanks for the clarification.

That helped me realize how i was thinking of A as a variable and not a constant.

Thanks,
Re: Number properties I question #2   [#permalink] 28 Nov 2009, 06:53
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Number properties I question #2

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