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Number properties I question #2

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Number properties I question #2 [#permalink]

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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?

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Re: Number properties I question #2 [#permalink]

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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, 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

Answer: (A)
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Re: Number properties I question #2 [#permalink]

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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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