Quadratic Equation Solver

Find the roots (x values) for $ax^2 + bx + c = 0$.

Equation Format:

$ax^2 + bx + c = 0$

Enter Coefficients A, B, and C

What is a Quadratic Equation?

A quadratic equation is a second-degree polynomial in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0. It is one of the most important concepts in algebra and is widely used in mathematics, physics, engineering, and finance.

The Quadratic Formula

To solve a quadratic equation, we use the formula:

x = [-b ± √(b² - 4ac)] / (2a)

Here, the value under the square root (b² - 4ac) is called the discriminant (Δ). The discriminant determines the nature of roots:

  • If Δ > 0 → Two distinct real roots
  • If Δ = 0 → One repeated real root
  • If Δ < 0 → Two complex conjugate roots

Examples of Solving Quadratic Equations

  • x² – 5x + 6 = 0 → Roots are x = 2 and x = 3
  • x² + 4x + 4 = 0 → Root is x = -2 (double root)
  • x² + x + 1 = 0 → Roots are complex numbers

Step-by-Step Method

  1. Identify the coefficients a, b, and c.
  2. Calculate the discriminant Δ = b² – 4ac.
  3. Apply the quadratic formula.
  4. Simplify to get one or two roots.

Applications of Quadratic Equations

Quadratic equations are not just theoretical. They are used in:

  1. Physics – Projectile motion, velocity, and energy problems
  2. Engineering – Design, structural analysis, and electronics
  3. Finance – Profit and loss curves, interest modeling
  4. Computer Science – Graphics, algorithms, and simulations
  5. Mathematics – Algebra, calculus, and higher-level studies

Frequently Asked Questions

1. Can this solver handle negative numbers?

Yes, quadratic equations with negative coefficients are fully supported.

2. Does it show complex roots?

Yes. If the discriminant is less than zero, the result will be complex roots.

3. Is this free to use?

Absolutely! You can use it unlimited times without any signup or fees.

4. What if a = 0?

If a = 0, then the equation is not quadratic, but a linear equation.

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Final Words

Our Quadratic Equation Solver is a fast, reliable, and free tool that helps you calculate roots instantly. Whether you are a student solving homework, a teacher preparing examples, or a professional working on equations, this solver provides accurate results with ease. Bookmark this page and use it anytime you need quick solutions to quadratic problems.

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