Q1
If the discriminant is negative, the quadratic equation has:
Ano real roots
Btwo real roots
Cexactly one real root
Dinfinite roots
CBSEClass 10 (CBSE)MathematicsCh 4 · Topic 2
The Quadratic Formula and Discriminant
Learning to solve any quadratic equation using the quadratic formula and determine the nature of roots.
Core concept
If the discriminant is positive, the equation has two distinct real roots; if it equals zero, the equation has exactly one repeated real root (a double root); and if it is negative, the equation has no real roots (only complex roots, not covered at this level). This formula provides a universal, reliable method for solving quadratics that works even when the roots are irrational or when factorisation would be very difficult to find by inspection.
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• Quadratic formula: x = [-b ± √(b²-4ac)] / 2a, solves any quadratic equation.
• Discriminant = b²-4ac, determines the nature of the roots.
• Positive discriminant: two distinct real roots. Zero: one repeated root. Negative: no real roots.
• The quadratic formula works even when factorisation is difficult or the roots are irrational.