CAT Preparation Online - Simple one from Quadratic Equations

Question

How many integer solutions exist for the equation x² - 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 x² 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.