Quadratic Equation Calculator

Quadratic Equation Solver

Solve quadratic equations ax² + bx + c = 0. Find real and complex roots with full step-by-step breakdown.

a (coefficient of x²) *

Must not be zero

b (coefficient of x) *

c (constant term) *

Root Format

Show Steps

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Quadratic Equation Roots

x₁

—

x₂

—

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Graph Visualization

Parabola showing roots and vertex

—

📋

Calculation Breakdown

Step-by-step quadratic solution

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Discriminant

—

Δ = b² - 4ac

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Nature of Roots

—

Real/Complex

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Vertex

—

(h, k)

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Sum of Roots

—

-b/a

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Quadratic Formulas

Key concepts and relationships

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Quadratic Tips

Understanding quadratic equations

📐 Mathematical Disclaimer: This quadratic equation solver uses the quadratic formula. For complex roots, results are expressed as a ± bi. Ensure a ≠ 0 for a valid quadratic equation.