Quadratic Equation Solver

The SolversPro Quadratic Equation Solver is a free browser-based algebra calculator that finds real or complex roots, evaluates the discriminant (Δ = b² - 4ac), and computes the parabolic vertex for any second-degree polynomial in real time.

ax² + bx + c = 0

Discriminant & Root Classification Reference

Standard analytical behavior of the discriminant (Δ = b² - 4ac) across second-degree polynomial curves.

Discriminant Condition Nature of Roots Parabolic X-Axis Intercepts Root Formula
Δ > 0 2 Distinct Real Roots Crosses x-axis at two points x = (-b ± √Δ) / 2a
Δ = 0 1 Repeated Real Root Touches x-axis at vertex point x = -b / 2a
Δ < 0 2 Complex Conjugate Roots No real x-axis intersection x = (-b ± i√|Δ|) / 2a

Frequently Asked Questions

The quadratic formula is x = (-b ± √(b² - 4ac)) / 2a. It provides the solutions (or roots) of a quadratic equation of the form ax² + bx + c = 0.

The discriminant is the part of the formula under the square root: Δ = b² - 4ac. It tells you the nature of the roots: if Δ > 0, there are 2 real roots. If Δ = 0, there is 1 real root. If Δ < 0, there are 2 complex/imaginary roots.

The vertex is the highest or lowest point on the graph of the quadratic equation (which is a parabola). The x-coordinate is found using -b / 2a, and the y-coordinate is the function's value at that x.

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