If ax² + bx + c = 0 then x =

If D = b² − 4ac ≥ 0 then the values of x are real

If D = b² − 4ac < 0 then the values of x are complex

|z| is always a positive real number regardless of x being a real number or complex number.

Given eqn. is |x|² + 3|x| + 2 = 0 and a = 1, b = 3 and c = 2

|x|² + 3|x| + 2 = 0

⇒ |x| =

⇒ |x| = 2 or −1

But |x| cannot be negative

No real root for the equation.