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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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Senior Manager
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Joined: 10 Oct 2018
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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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19 Mar 2019, 05:17
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65% (hard)

Question Stats:

43% (01:36) correct 57% (01:24) wrong based on 53 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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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
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Joined: 18 Jan 2019
Posts: 28
Re: What is the range of values for z^2 given that (z^2+4)(z^2-2)<0  [#permalink]

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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

can you explain why A is wrong? the values in this range satisfy the condition
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Posts: 5031
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Concentration: Sustainability, Marketing
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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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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

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.
Intern
Joined: 18 Jan 2019
Posts: 28
Re: What is the range of values for z^2 given that (z^2+4)(z^2-2)<0  [#permalink]

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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

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

Yeah you are right, I forgot about -2, thanks
Intern
Joined: 22 Sep 2018
Posts: 20
Re: What is the range of values for z^2 given that (z^2+4)(z^2-2)<0  [#permalink]

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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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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.

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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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