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Online Quadratic Equation Calculator
Solve quadratic equations quickly and accurately using our online quadratic equation calculator. Calculates real and complex roots based on the discriminant of the equation.
| Equation | 1x2 + 8x + 12 = 0 |
|---|---|
| Solution | x = -2 or -6 |
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What Is This Tool?
This calculator solves quadratic equations of the form ax² + bx + c = 0 using the quadratic formula. It determines the roots by computing the discriminant and provides both real and complex solutions with high precision.
How to Use This Tool?
- Enter the coefficient values for a, b, and c in the respective input fields.
- Ensure that coefficient a is not zero to form a valid quadratic equation.
- Click the 'Calculate' button to solve the equation.
- Review the displayed discriminant to understand the type of roots.
- View the calculated solutions provided by the tool.
Key Features
- Solves quadratic equations using the standard quadratic formula.
- Determines the nature of roots based on the discriminant value.
- Provides up to two real or two complex solutions accordingly.
- Utilizes precise floating-point arithmetic for accuracy.
- Simple, easy-to-use browser-based interface.
Examples
- Solve 2x² - 4x - 6 = 0: Compute discriminant D = (-4)² - 4(2)(-6) = 64, then apply the formula x = (4 ± 8) / 4, resulting in solutions x₁ = 3 and x₂ = -1.
Common Use Cases
- Students and educators solving algebra homework and teaching quadratic equations.
- Engineers analyzing parabolic trajectories and optimization problems.
- Scientists and programmers dealing with quadratic relationships in physics or data analysis.
Tips & Best Practices
- Double-check that coefficient a is not zero before calculation.
- Input numerical coefficients carefully to avoid errors.
- Interpret the discriminant to understand whether solutions are real or complex.
- Use the tool to verify manual calculations for accuracy.
- Be aware of floating-point precision limitations with extremely large coefficients.
Limitations
- Coefficient a must be non-zero for the equation to be quadratic.
- Very large or small input values may lead to floating-point rounding errors.
- Complex solutions are displayed numerically and not as symbolic expressions.
Frequently Asked Questions
- What happens if the discriminant is negative?
- When the discriminant is less than zero, the equation has two complex solutions which are shown numerically by the calculator.
- Can this calculator handle any quadratic equation?
- The calculator solves any quadratic equation where the coefficient a is not zero and coefficients are within floating-point precision limits.
- How is the discriminant used in solving quadratics?
- The discriminant determines the type and number of solutions: positive for two real roots, zero for one repeated real root, and negative for two complex roots.
Key Terminology
- a
- Coefficient of x² in the quadratic equation.
- b
- Coefficient of x in the quadratic equation.
- c
- Constant term in the quadratic equation.
- Discriminant (D)
- Value calculated as b² - 4ac that determines the nature of quadratic roots.
- Roots (x)
- Solutions of the quadratic equation found using the quadratic formula.