Nature of Roots

Complex roots are non-real roots that exist in pairs and are conjugates of each other (e.g., x = a + bi and x = a - bi)

Calculate the discriminant Δ and use its value to identify the root type.

Δ > 0 : Two distinct real roots. Δ = 0 : One repeated real root. Δ < 0 : Two complex roots.

The discriminant Δ = b²-4ac determines the nature of the roots of a quadratic equation.