Quadratic Formula Calculator
Solve quadratic equations
Frequently Asked Questions
What is the quadratic formula?
The quadratic formula solves ax² + bx + c = 0: x = (-b ± √(b²-4ac)) / (2a). Enter coefficients a, b, and c to find both solutions. For x² - 5x + 6 = 0: x = (5 ± √1) / 2, giving x = 3 and x = 2.
What is the discriminant and what does it tell me?
The discriminant is D = b² - 4ac. If D > 0: two distinct real roots. If D = 0: one repeated real root. If D < 0: two complex conjugate roots. The calculator shows the discriminant value and root type.
How do I find the vertex of a parabola?
The vertex x-coordinate is x = -b/(2a). Substitute back to find y. For y = 2x² - 8x + 3: vertex x = 8/4 = 2, y = 2(4) - 16 + 3 = -5. Vertex is at (2, -5). The calculator shows the vertex coordinates.
What are complex roots?
When the discriminant is negative, roots involve imaginary numbers. For x² + x + 1 = 0: D = 1-4 = -3, roots are (-1 ± i√3)/2. The calculator displays complex roots in a+bi form.
Can I solve higher-degree polynomials?
This calculator solves degree-2 (quadratic) equations. For cubic (degree 3) and quartic (degree 4) equations, different formulas exist. Degree 5 and above have no general algebraic solution (Abel-Ruffini theorem).