Determine the nature of the roots of the quadratic equation 3x² + 2x + 5 = 0.

Correct option is A

Given:

​$$3x^2 + 2x + 5 = 0$$​​

Concept Used:

To determine the nature of the roots of a quadratic equation, we calculate the discriminant Δ, given by the formula:

Δ = $$b^2 - 4ac$$​​

where a, b, and c are the coefficients of the quadratic equation $$ax^2 + bx + c = 0$$​​

If Δ > 0, the roots are real and distinct.

If Δ = 0, the roots are real and equal.

If Δ < 0, the roots are complex (imaginary)

Solution:

For the equation $$3x^2 + 2x + 5 = 0$$​, we have:

a = 3, b = 2, and c = 5

Now,

​$$\Delta = b^2 - 4ac = 2^2 - 4(3)(5) = 4 - 60 = -56$$​​

Since Δ = -56 which is less than 0, the roots are complex.

Thus, the nature of the roots is complex (imaginary)