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m13/q23....wrong ans

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m13/q23....wrong ans [#permalink]

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New post 03 Jan 2010, 08:27
Is A positive?

i)x^2-2x+A is positive for all x
ii)Ax^2+1 is positive for all x
reason given < Statement (1) by itself is sufficient. x^2-2x+A = (x-1)^2+(A-1) . For this expression to be always positive (A-1) has to be more than 0.so A has to be more than 1>
A can be any -ive int till (x-1)^2 is greater than (A-1)... ex x=3... 4+A-1>0.. or A>-3
ans shud be E...pl confirm
i think where we have gone wrong is taking + in(x-1)^2+(A-1) as *....
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6141 [0], given: 121

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Re: m13/q23....wrong ans [#permalink]

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New post 03 Jan 2010, 17:13
chetan2u wrote:
Is A positive?

i)x^2-2x+A is positive for all x
ii)Ax^2+1 is positive for all x
reason given < Statement (1) by itself is sufficient. x^2-2x+A = (x-1)^2+(A-1) . For this expression to be always positive (A-1) has to be more than 0.so A has to be more than 1>
A can be any -ive int till (x-1)^2 is greater than (A-1)... ex x=3... 4+A-1>0.. or A>-3
ans shud be E...pl confirm
i think where we have gone wrong is taking + in(x-1)^2+(A-1) as *....


Step by step:

Question: is \(A>0\)?

(1) \(x^2-2x+A\) is positive for all \(x\):

\(f(x)=x^2-2x+A\) is a function of of upward parabola. We are told that it's positive for all \(x\) --> \(f(x)=x^2-2x+A>0\), which means that this function is "above" X-axis OR in other words parabola has no intersections with X-axis OR equation \(x^2-2x+A=0\) has no real roots.

Quadratic equation to has no real roots discriminant must be negative --> \(D=2^2-4A=4-4A<0\) --> \(1-A<0\) --> \(A>1\).

Sufficient.

(2) \(Ax^2+1\) is positive for all \(x\):

\(Ax^2+1>0\) --> when \(A\geq0\) this expression is positive for all \(x\). So \(A\) can be zero too.

Not sufficient.

So I think the answer (A) is correct.
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Kudos [?]: 135777 [0], given: 12711

Expert Post
Math Expert
User avatar
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Joined: 02 Aug 2009
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Re: m13/q23....wrong ans [#permalink]

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New post 04 Jan 2010, 03:43
hi .....
i do understand that as an eq of parabola c would be y-intercept and parabola being limited to i and ii quad , c would be always +ive...... but why cant we prove it taking it as a normal eq (as it wud seem to any layperson)... is there any way to prove it
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6141 [0], given: 121

Re: m13/q23....wrong ans   [#permalink] 04 Jan 2010, 03:43
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