The nature of the roots of the quadratic equation  $$x^2 + 4x + 8 = 0$$​ is:

Correct option is D

Given:

The quadratic equation is $$x^2 + 4x + 8 = 0$$​​

Concept Used:
The nature of the roots of a quadratic equation $$ax^2 + bx + c = 0$$​ can be determined using the discriminant Δ, given by:

​$$Δ = b^2 - 4ac$$​​

If Δ > 0, the equation has two distinct real roots.

If Δ = 0, the equation has exactly one real root (repeated root).

If Δ < 0, the equation has two complex (imaginary) roots.

Solution:
For the equation $$x^2 + 4x + 8 = 0$$​, we have:

a = 1, b = 4, c = 8

Calculate the discriminant:

Δ = 42 − 4(1)(8)

=16 − 32 = −16

Since Δ = −16, which is less than 0.

Thus, the nature of the roots is complex or not real roots(imaginary).