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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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Is A positive? 1. x^2-2*x+A is positive for all x 2. A*x^2+1 [#permalink] New post 28 Aug 2005, 00:48
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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

Please explain your answers.
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Re: DS Yes/No [#permalink] New post 28 Aug 2005, 04:52
Edited

My bad

cond 1) A could be + or - depending upon th value of x^2-2*x

cond 2) A Could still be + or -....

Combining both I think E
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Last edited by ranga41 on 30 Aug 2005, 15:42, edited 1 time in total.
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Re: DS Yes/No [#permalink] New post 28 Aug 2005, 05:50
ranga41 wrote:
B.
cond 1) A could be + or - depending upon th value of x^2-2*x
cond 2) A should be + since x^2 is always positive..


Ranga,
B cannot be true. if x=0.1, A=-1, A*x^2+1 is still psitive. i doubt A too. So it should be E. no wonder if it is A.
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 [#permalink] New post 28 Aug 2005, 09:21
A

"x^2-2x+A > 0 for all x" means the equation
x^2-2x+A = 0 has no real number solution, i.e., (-2)^2 - 4*1*A < 0
or A > 1
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Re: DS Yes/No [#permalink] New post 28 Aug 2005, 11:16
2 first: X^2 must be positive for all x=/=0
1 is positive
If A is positive, then good, 2 works
But if A is 0, then we get 1 as answer.

Therefore, 'A' could be 0 or +ve. Out

1 Next: X^2 must be positive for all X=/=0
(-2x will be positive for all negative x)
So, 'A' may be -ve and the value in (1) still remains positive
'A' may also be -ve

Combining, 'A' may be a negative fraction e.g. (-0.0003) and will not work if (x > 2)

So, i'm on (E)
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 [#permalink] New post 28 Aug 2005, 12:03
qpoo wrote:
A. "x^2-2x+A > 0 for all x" means the equation
x^2-2x+A = 0 has no real number solution, i.e., (-2)^2 - 4*1*A < 0
or A > 1


from i, suppose x = -1, then A can be +ve or -ve. how is it? not clear.
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 [#permalink] New post 29 Aug 2005, 11:47
HIMALAYA wrote:
qpoo wrote:
A. "x^2-2x+A > 0 for all x" means the equation
x^2-2x+A = 0 has no real number solution, i.e., (-2)^2 - 4*1*A < 0
or A > 1


from i, suppose x = -1, then A can be +ve or -ve. how is it? not clear.


we are proving if A is > 0 , then all X will make:
x^2-2*x+A > 0 not the other way around, IMO
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 [#permalink] New post 30 Aug 2005, 00:39
Im going for C.

1) can be ruled out as x^2 - 2x >0 so A can be + or -ve
2) can be ruled out since if x<1, A can be-ve and statement still satisfied.

Taking both together- A will have to be positive for both statements to hold true. A can only be neagtive in statement 2 if x <1. but if x<1 then x^2 -2x from statement 1 will be < 0 so A willk NEED to be +ve to make this statement true.

remember the 2 statements ALWAYS are to be >0 no matter what value of x. the answer will be E, if for a certain value of x, A can be negative and both statements hold true. i dont think this can happen.

whts OA/OE?[/b]
  [#permalink] 30 Aug 2005, 00:39
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