What describes the nature of the roots when the discriminant is less than zero?

When the discriminant of a quadratic equation is less than zero, it indicates that the quadratic does not intersect the x-axis. The discriminant, found from the formula ( b^2 - 4ac ) in the context of the quadratic equation ( ax^2 + bx + c = 0 ), is a critical component in determining the nature of the roots.

A negative discriminant signifies that the expression under the square root in the quadratic formula ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ) results in a negative value, which leads to imaginary results. Therefore, the roots are not real numbers but rather complex numbers with non-zero imaginary parts, specifically described as two distinct imaginary roots. This means that the roots can be expressed in the form ( p \pm qi ), where both ( p ) and ( q ) are real numbers, and ( q ) is not equal to zero.

Thus, the nature of the roots when the discriminant is less than zero is characterized as two imaginary roots.