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If z^2-4<0, What is the value of z [#permalink]
 24 Nov 2003, 11:52
Question Stats:
66% (01:50) correct
33% (00:02) wrong based on 0 sessions
If z^2-4<0, What is the value of z?
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Intern
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Not sure if this is GMAT type material [#permalink]
24 Nov 2003, 13:34
-2<z<2
obviously.
Solving it algebraically is tricky unless you know how to deal with inequalities using the number line test method.
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Manager
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yes, -2<Z<2
i find number line test to be the best method for these types of problems...any other quick simple ways??
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VP
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think, I screwed myself here 
yes, you are right..it should be -2<Z<2
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Director
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It's unanimous! -2<z<2. Unless we're the masses of ...
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Intern
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What is number line test method?
How is it used?
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Rocky
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Manager
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I think the answer is evident when you move the 4 over to the other side.
z^2 <4> z > -2 but < 2 , the range of values as mentioned by others is: -2<z<2
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Intern
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but no body explained whts a number line test method?
sabita
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ann wrote: If z^2-4<0, What is the value of z? sabitamishra1 wrote: but no body explained whts a number line test method?
sabita z^2 - 4 <0 z^2 < 4 since z^2 is +ve, it is >0 but less than 4. so z must be in between -2 and 2 excluding. if you draw a line and put these values on the number line, you will see where z lies.
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Director
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ann wrote: If z^2-4<0, What is the value of z? whats wrong with this approach? (z+2)(z-2) < 0 z+2 < 0 or z-2 < 0 z < - 2 OR z < 2
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Director
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Z^2<4
sqrt(z^2) <sqrt(4)
=> |Z|<2
=> -2<Z<2
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SVP
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=> (z-2)(z+2) < 0 => -2 < z < 2
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Manager
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z^2<4
So z will lie between 2 and -2
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Manager
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Same as above
Z^2-4 < 0 add 4 to both sides
z^2 < 4 Take the square root of both sides
z < 2 and z > -2 Remember when you take the square root of an inequality, the negative sign flips the inequality
so -2<z<2
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