Back to Quadratic Relations
The discriminant: how many real roots?
Questions at easy, medium and hard levels. Pick a level and get a fresh set every time, with instant feedback.
Learn it The discriminant D = b² − 4ac tells you how many real roots ax² + bx + c = 0 has, without solving: D > 0 → two roots, D = 0 → one (repeated) root, D < 0 → no real roots. It also tells you how many times the parabola crosses the x-axis.
Example: How many roots does 2x² − 3x + 5 = 0 have?
- D = (−3)² − 4(2)(5) = 9 − 40 = −31.
- D < 0, so no real roots.
Loading questions…