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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
Guia passo a passo
- 1Enter coefficients a, b, c from ax² + bx + c = 0
- 2Calculate b² - 4ac
- 3Interpret the sign and value
Exemplos resolvidos
Entrada
x² - 5x + 6 = 0
Resultado
Δ = 1 (two distinct real roots)
25 - 24 = 1
Erros comuns a evitar
- ✕Sign errors in b or c
- ✕Forgetting the 4ac term
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