The nature of the roots depends on the quantity under the square root sign i.e. b2 – 4ac. This quantity is called the discriminant of the equation and usually denoted by D.
Let the quadratic equation be ax2 + bx + c = 0, a ≠ 0 and a, b, c ∈ R.
∴ Discriminant (D) = b2 – 4ac.
Then a quadratic equation has :
(i) Two real and unequal roots if b2 – 4ac > 0
(ii) Two real and equal roots if b2 – 4ac = 0
(iii) Two unreal and unequal roots if b2 – 4ac < 0
(iv) Two real roots if b2 – 4ac ≥ 0