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Quadratic Equation Solver

Quadratic equations form parabolas in physics and engineering. This solver computes real and complex conjugate roots using the quadratic formula.

What Is the Quadratic Equation Solver?

A Quadratic Equation Solver finds solutions for second-degree polynomials.

How Does the Quadratic Equation Solver Work?

Evaluates discriminant and solves roots.

Quadratic Equation Solver Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Standard quadratic formula.

How to Use the Quadratic Equation Solver

  1. Enter coefficients a, b, and c.

Step-by-Step Example Calculation

x² − 5x + 6 = 0

Input Values:

a:1
b:-5
c:6
Worked Steps: Δ = 1; Roots are x₁ = 3, x₂ = 2.

Understanding Your Result

Shows root values and discriminant.

Factors That Affect the Result

  • Signs and magnitudes of coefficients.

When Should You Use This Calculator?

  • Physics trajectories, engineering optimization, and algebra.

Assumptions & Limitations

  • Second-degree polynomial (a ≠ 0).

Frequently Asked Questions

Calculation Accuracy & Reference Note

Double-precision math.

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