Quadratic equations and discriminant basics – UGC NET Question

A, B, C and E are all correct statements about quadratic equations and their discriminant. A states the general form with a ≠ 0, B defines the discriminant, C correctly says that Δ 0 yields two distinct real roots. D is wrong because Δ = 0 gives equal (repeated) real roots, not two distinct roots. Hence the combination containing A, B, C and E only is correct.

Option A:
Option A includes A, B and C, all of which are true, but omits E, which correctly describes the case Δ > 0. Because it misses one more true statement, this option does not capture the full set of correct statements.

Option B:
Option B adds D to A, B and C, but D is false since Δ = 0 leads to equal roots, not distinct ones. Including a false statement makes this combination incorrect even though it contains many true statements.

Option C:
Option C is correct because it lists exactly the true statements A, B, C and E and excludes D, the only incorrect one. It therefore fully reflects the standard classification of roots using the discriminant.

Option D:
Option D selects B, D and E, but by including D it wrongly treats Δ = 0 as giving distinct roots and also omits A and C, which are true. This combination is therefore both incomplete and partially wrong.