If ax2 + bx + c = 0 then x \(=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)
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| = \(\frac{-3\pm\sqrt{9-8}}{2}\)
⇒ |x| = 2 or −1
But |x| cannot be negative
No real root for the equation.