Let D denote the discriminant $$b^{2}-4ac$$. Hence, depending on the sign and value of D, nature of the roots would be as follows:
- D < 0 → Complex (imaginary) roots
- D = 0 → Real, equal roots: x = −b/2a
- D > 0, perfect square → Real, rational, unequal
- D > 0, not a perfect square → Real, irrational, unequal (conjugate surds)
If roots are irrational or complex, they always occur in conjugate pairs
