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# Number properties I question #2

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Manager
Joined: 08 Nov 2009
Posts: 59

Kudos [?]: 9 [0], given: 3

Location: United States
Concentration: Strategy, Sustainability
WE: Supply Chain Management (Hospitality and Tourism)
Number properties I question #2 [#permalink]

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27 Nov 2009, 14:43
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,

Kudos [?]: 9 [0], given: 3

Joined: 20 Aug 2009
Posts: 305

Kudos [?]: 165 [1], given: 69

Location: Tbilisi, Georgia
Schools: Stanford (in), Tuck (WL), Wharton (ding), Cornell (in)
Re: Number properties I question #2 [#permalink]

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28 Nov 2009, 02:45
1
KUDOS
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, so$$A>0$$, 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

Kudos [?]: 165 [1], given: 69

Manager
Joined: 08 Nov 2009
Posts: 59

Kudos [?]: 9 [0], given: 3

Location: United States
Concentration: Strategy, Sustainability
WE: Supply Chain Management (Hospitality and Tourism)
Re: Number properties I question #2 [#permalink]

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28 Nov 2009, 07:53
Thanks for the clarification.

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

Thanks,

Kudos [?]: 9 [0], given: 3

Re: Number properties I question #2   [#permalink] 28 Nov 2009, 07:53
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# Number properties I question #2

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