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The discriminant (Δ = b² - 4ac) of a quadratic equation determines the nature and number of roots. It tells whether solutions are real, complex, or repeated.

Fórmula

Δ = b² - 4ac; if Δ > 0: two real roots, Δ = 0: one repeated root, Δ < 0: complex roots

Guía paso a paso

1Enter coefficients a, b, c from ax² + bx + c = 0
2Calculate b² - 4ac
3Interpret the sign and value

Ejemplos resueltos

Entrada

x² - 5x + 6 = 0

Resultado

Δ = 1 (two distinct real roots)

25 - 24 = 1

Errores comunes a evitar

✕Sign errors in b or c
✕Forgetting the 4ac term

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