Resolvedor de Equacoes do Segundo Grau Gratis
Resolva qualquer equacao quadratica ax² + bx + c = 0. Encontre solucoes reais e complexas com os passos.
Root1
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Formula
## How to Solve a Quadratic Equation ### Quadratic Formula **x = (-b ± sqrt(b² - 4ac)) / (2a)** For the equation ax² + bx + c = 0: 1. Calculate the **discriminant**: D = b² - 4ac 2. If D > 0: two distinct real roots 3. If D = 0: one repeated real root 4. If D < 0: no real roots (complex roots) ### Vertex The vertex of the parabola is at x = -b/(2a), y = c - b²/(4a).
Exemplo Resolvido
Solve x² - 5x + 6 = 0.
- 01D = (-5)² - 4(1)(6) = 25 - 24 = 1
- 02x₁ = (5 + √1) / 2 = 6/2 = 3
- 03x₂ = (5 - √1) / 2 = 4/2 = 2
- 04Roots are x = 3 and x = 2
Perguntas Frequentes
What is the quadratic formula?
x = (-b ± √(b² - 4ac)) / (2a). It gives the solutions to any quadratic equation ax² + bx + c = 0.
What does the discriminant tell you?
The discriminant (b² - 4ac) reveals the nature of the roots: positive means two real roots, zero means one repeated root, negative means complex roots.
What if a = 0?
If a = 0, the equation is linear (bx + c = 0), not quadratic. The solution is x = -c/b.
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