Quadratic Calculator

Solve quadratic equations step by step with explanations and graph analysis.

Enter Quadratic Equation

Equation: x² + 2x + 1 = 0

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About Quadratic Equations

What is a Quadratic Equation?

A quadratic equation is a polynomial equation of degree 2, typically written in the form ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0.

How to Solve Quadratic Equations

  1. Quadratic Formula: x = (-b ± √(b² - 4ac)) / (2a)
  2. Factoring: Write the equation as (px + q)(rx + s) = 0
  3. Completing the Square: Rewrite in the form (x + p)² = q
  4. Graphical Method: Find where the parabola intersects the x-axis

Applications in Real Life

  • Physics: Projectile motion and free fall
  • Engineering: Structural analysis and optimization
  • Economics: Cost and revenue analysis
  • Biology: Population growth models

Frequently Asked Questions

What is the discriminant?

The discriminant is b² - 4ac. It determines the nature of the roots: positive (two real roots), zero (one real root), or negative (two complex roots).

When do quadratic equations have no real solutions?

When the discriminant is negative (b² - 4ac < 0), the equation has two complex conjugate roots.