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Quadratic Equation Solver

Solve equations of the form ax² + bx + c = 0

Equation:

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Discriminant:

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Roots:

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Solution Steps:

Enter coefficients to see solution steps

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About Quadratic Equations

A quadratic equation is any equation that can be written in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

How to Use This Tool

  1. Enter the coefficient a (the coefficient of x²)
  2. Enter the coefficient b (the coefficient of x)
  3. Enter the coefficient c (the constant term)
  4. Click the "Solve Equation" button
  5. View the equation, discriminant, roots, and step-by-step solution

Why We Use This Tool

  • Educational aid: Understand the quadratic formula and solution process
  • Problem-solving: Quickly solve quadratic equations for homework or exams
  • Verification: Check your manual calculations for accuracy
  • Applications: Solve real-world problems in physics, engineering, and economics

Quadratic Formula

The solutions to any quadratic equation can be found using the quadratic formula:

x = [-b ± √(b² - 4ac)] / 2a

Discriminant

The discriminant (D = b² - 4ac) determines the nature of the roots:

  • D > 0: Two distinct real roots
  • D = 0: One real root (repeated)
  • D < 0: Two complex roots

Examples

Example 1: x² - 3x + 2 = 0

Solutions: x = 1, x = 2

Example 2: x² + 4x + 4 = 0

Solution: x = -2 (double root)

Example 3: x² + x + 1 = 0

Solutions: Complex roots