Write the sum of real roots of the equation x 2 + |x| – 6 = 0.

Question

Philoid · Accepted Answer

First of all, the equation is x² + |x| − 6 = 0

CASE 1: x>0 then |x| = x

⇒ x² + x− 6 = 0

⇒ x² + 3x – 2x – 6 = 0

⇒ (x + 3)(x−2) = 0

⇒ x = 2, – 3

CASE 2: x<0 |x| = – x

⇒ x²−x−6 = 0

⇒ x² − 3x + 2x−6 = 0

⇒ (x−3)(x + 2) = 0

⇒ x = −2, 3

So the sum of the roots is 2 + (– 3) + (– 2) + 3

= 0