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What is the range of values for z^2 given that (z^2+4)(z^2-2)<0

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What is the range of values for z^2 given that (z^2+4)(z^2-2)<0  [#permalink]

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New post 19 Mar 2019, 05:17
2
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A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

39% (01:46) correct 61% (01:30) wrong based on 38 sessions

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What is the range of values for \(x^2\) given that (\(x^2\)+4)(\(x^2\)-2)<0?
(A) -4 < \(x^2\) < 2
(B) 0 ≤ \(x^2\) ≤ 2
(C) 0 ≤ \(x^2\) < 2
(D) 0 < \(x^2\) < 2
(E) -∞ < x < 2

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Re: What is the range of values for z^2 given that (z^2+4)(z^2-2)<0  [#permalink]

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New post 26 Mar 2019, 10:17
nm97 wrote:
What is the range of values for \(x^2\) given that (\(x^2\)+4)(\(x^2\)-2)<0?
(A) -4 < \(x^2\) < 2
(B) 0 ≤ \(x^2\) ≤ 2
(C) 0 ≤ \(x^2\) < 2
(D) 0 < \(x^2\) < 2
(E) -∞ < x < 2


basic clue or trick to solve this question is to check our desired outcome using given options
we need is (\(x^2\)+4)(\(x^2\)-2)<0
so x has to be <2 ; it cannot be =2 as then (\(x^2\)+4)(\(x^2\)-2)<0 wont stand true
so negate options A,B
also
value x^2 cannot be-ve so option E negated
between option C & D
we can note that (\(x^2\)+4)(\(x^2\)-2)<0 will hold true when x^2=0 so IMO C is correct :cool:
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Re: What is the range of values for z^2 given that (z^2+4)(z^2-2)<0  [#permalink]

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New post 26 Mar 2019, 23:28
Archit3110 wrote:
nm97 wrote:
What is the range of values for \(x^2\) given that (\(x^2\)+4)(\(x^2\)-2)<0?
(A) -4 < \(x^2\) < 2
(B) 0 ≤ \(x^2\) ≤ 2
(C) 0 ≤ \(x^2\) < 2
(D) 0 < \(x^2\) < 2
(E) -∞ < x < 2


basic clue or trick to solve this question is to check our desired outcome using given options
we need is (\(x^2\)+4)(\(x^2\)-2)<0
so x has to be <2 ; it cannot be =2 as then (\(x^2\)+4)(\(x^2\)-2)<0 wont stand true
so negate options A,B
also
value x^2 cannot be-ve so option E negated
between option C & D
we can note that (\(x^2\)+4)(\(x^2\)-2)<0 will hold true when x^2=0 so IMO C is correct :cool:


can you explain why A is wrong? the values in this range satisfy the condition
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What is the range of values for z^2 given that (z^2+4)(z^2-2)<0  [#permalink]

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New post 26 Mar 2019, 23:32
Ish1996 wrote:
Archit3110 wrote:
nm97 wrote:
What is the range of values for \(x^2\) given that (\(x^2\)+4)(\(x^2\)-2)<0?
(A) -4 < \(x^2\) < 2
(B) 0 ≤ \(x^2\) ≤ 2
(C) 0 ≤ \(x^2\) < 2
(D) 0 < \(x^2\) < 2
(E) -∞ < x < 2


basic clue or trick to solve this question is to check our desired outcome using given options
we need is (\(x^2\)+4)(\(x^2\)-2)<0
so x has to be <2 ; it cannot be =2 as then (\(x^2\)+4)(\(x^2\)-2)<0 wont stand true
so negate options A,B
also
value x^2 cannot be-ve so option E negated
between option C & D
we can note that (\(x^2\)+4)(\(x^2\)-2)<0 will hold true when x^2=0 so IMO C is correct :cool:


can you explain why A is wrong? the values in this range satisfy the condition


the range option A does not satisfy the inequality...
see we need a range where we get values<0 ; so substitute different values and you shall get the answer.
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Re: What is the range of values for z^2 given that (z^2+4)(z^2-2)<0  [#permalink]

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New post 26 Mar 2019, 23:50
Ish1996 wrote:
Archit3110 wrote:
nm97 wrote:
What is the range of values for \(x^2\) given that (\(x^2\)+4)(\(x^2\)-2)<0?
(A) -4 < \(x^2\) < 2
(B) 0 ≤ \(x^2\) ≤ 2
(C) 0 ≤ \(x^2\) < 2
(D) 0 < \(x^2\) < 2
(E) -∞ < x < 2


basic clue or trick to solve this question is to check our desired outcome using given options
we need is (\(x^2\)+4)(\(x^2\)-2)<0
so x has to be <2 ; it cannot be =2 as then (\(x^2\)+4)(\(x^2\)-2)<0 wont stand true
so negate options A,B
also
value x^2 cannot be-ve so option E negated
between option C & D
we can note that (\(x^2\)+4)(\(x^2\)-2)<0 will hold true when x^2=0 so IMO C is correct :cool:


can you explain why A is wrong? the values in this range satisfy the condition


Yeah you are right, I forgot about -2, thanks
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Re: What is the range of values for z^2 given that (z^2+4)(z^2-2)<0  [#permalink]

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New post 30 Mar 2019, 10:30
nm97 wrote:
What is the range of values for \(x^2\) given that (\(x^2\)+4)(\(x^2\)-2)<0?
(A) -4 < \(x^2\) < 2
(B) 0 ≤ \(x^2\) ≤ 2
(C) 0 ≤ \(x^2\) < 2
(D) 0 < \(x^2\) < 2
(E) -∞ < x < 2


In the equation (x^2 + 4)(x^2-2)<0..either (X^2 + 4) is negative or (x^2 - 2) is negative.

Clearly X^2+4 can never be negative. So X^2-2 is negative

X^2-2<0

x^2<2...only option C seems to agree with the equation
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What is the range of values for z^2 given that (z^2+4)(z^2-2)<0  [#permalink]

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New post 30 Mar 2019, 11:33
Given, (x^2+4)(x^2-2)<0

So, in between (x^2+4) and (x^2-2), one expression must be positive and the other one must be negative.

Since x^2=a square value=always Non negative, (x^2+4) must be positive and (x^2-2) must be negative.

Thus, (x^2-2)<0
Or, x^2<2
So, x^2 must be less then 2 and since x^2 is a square value, it must be NON negative.

X^2 must be 0 or greater than 0 but less than 2.

My answer is C.

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What is the range of values for z^2 given that (z^2+4)(z^2-2)<0   [#permalink] 30 Mar 2019, 11:33
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