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quadratic inequalities

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quadratic inequalities

by meh » Mon Dec 23, 2013 1:57 am
4 - (x^2) ≥ 0

Way to do it...

-1( (x^2) - 4 ) ≥ 0
(x^2) - 4 ≤ 0
x^2 ≤ 4
|x| ≤ 2
-2 ≤ x ≤ 2

One question:

1) If this is the best way to do it...why ever factor to make (x-2)(x+2) in any problem (inequality or not)? Doesn't the GMAT warn against directly solving for x in quadratics without factoring?
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Source: — Data Sufficiency |
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by theCodeToGMAT » Mon Dec 23, 2013 4:40 am
It is important to do factorizing so that we may not neglect some possible value:

For example:
x - xy = 0
If we factorize:
x(1-y) = 0
either x = 0 & y = 1

Without Factorizing
x = xy
y = 1 ...

Here, we are left with one lesser value..
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