### CAT Preparation Online - Simple one from Quadratic Equations

**Question**

How many integer solutions exist for the equation x

^{2}- 8|x| - 48 =0?

**Explanation**

One approach is to solve when x > 0 and then solve for x < 0. However, there is a slightly simpler method.

Note that x

^{2}is the same as |x|^{2}, so we can treat the equation as a quadratic in |x|.
Or, |x|

^{2 }– 8|x| - 48 = 0
(|x| - 12|) (|x| + 4) = 0

|x| could be 12. |x| cannot be -4.

If |x| could be 12, x can be -12 and 12.

Two possible solutions exist.

Labels: CAT - Linear Quadratic Equations Questions and Solutions, CAT 2015, CAT 2016, CAT classes Chennai, CAT Online Classes, CAT Online Coaching, CAT Online Preparation, CAT preparation, CAT Quadratic Equations

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