Algebra • Mathematics • Engineering

Quadratic Equation SolverSolve ax² + bx + c = 0 • Step-by-Step Solutions • Discriminant Analysis

Quadratic Formula

Discriminant Analysis

Step-by-Step

Root Classification

Quick Example Equations:

Quadratic Equation Solver

Algebraic computation

ax² + bx + c = 0

Standard quadratic equation form

Coefficient a (x² term)

Coefficient of x² (must be non-zero for quadratic equation)

Coefficient b (x term)

Coefficient of x (can be zero)

Coefficient c (constant)

Constant term (can be zero)

Common Quadratic Forms

Standard form: ax² + bx + c = 0 where a ≠ 0

Graph is always a parabola (U-shaped curve)

Can have 0, 1, or 2 real solutions depending on discriminant

If a < 0, parabola opens downward; if a > 0, opens upward

Projectile motion follows quadratic patterns

Area problems often lead to quadratic equations

Profit maximization in business uses quadratic models

Signal processing and engineering rely on these equations

Δ > 0Two real distinct roots

Δ = 0One repeated real root

Δ < 0Two complex conjugate roots

Understanding the Quadratic Formula