Calcolatore della Formula Quadratica Gratuito
Risolvi equazioni di secondo grado con la formula quadratica. Trova le radici, il discriminante e il vertice.
Coefficient of x²
Coefficient of x
Constant term
Root1
3.000000
Formula
How to Use the Quadratic Formula
Formula
x = (-b ± √(b² - 4ac)) / (2a)
For the equation ax² + bx + c = 0
Discriminant (Δ = b² - 4ac)
Vertex
The vertex of the parabola is at x = -b/(2a), y = f(-b/(2a)).
Esempio Risolto
Solve x² - 5x + 6 = 0 (a=1, b=-5, c=6).
- 01Discriminant = (-5)² - 4(1)(6) = 25 - 24 = 1
- 02Since Δ > 0, there are two distinct real roots
- 03x₁ = (5 + √1) / 2 = 6 / 2 = 3
- 04x₂ = (5 - √1) / 2 = 4 / 2 = 2
- 05Vertex: x = 5/2 = 2.5, y = (2.5)² - 5(2.5) + 6 = -0.25
Domande Frequenti
What is the quadratic formula?
The quadratic formula x = (-b ± √(b²-4ac)) / (2a) finds the solutions (roots) of any quadratic equation ax² + bx + c = 0.
What does the discriminant tell us?
The discriminant (b²-4ac) tells you the nature of the roots: positive = 2 real roots, zero = 1 repeated root, negative = no real roots (2 complex roots).
What if the discriminant is negative?
If the discriminant is negative, the equation has no real solutions. The roots are complex numbers. This calculator shows the real part when the discriminant is negative.
Impara