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Online Quadratic Formula Calculator
Easily solve quadratic equations using the quadratic formula calculator. Identify real or complex roots quickly and accurately with this fast, user-friendly math tool.
ax2+bx+c=0
x =
-
6
11
±
√19i
11
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What Is This Tool?
This calculator solves quadratic equations of the standard form ax² + bx + c = 0 by applying the quadratic formula. It delivers exact solutions for the variable x, whether the roots are real or complex.
How to Use This Tool?
- Enter the coefficient values for a, b, and c from your quadratic equation
- Click the calculate button to process the inputs
- View the solutions for x, which may include real or complex numbers
- Review the discriminant value to understand the nature of the roots
Key Features
- Solves quadratic equations using the quadratic formula
- Handles both real and complex roots accurately
- Uses double-precision floating-point arithmetic for precise results
- Simple input for coefficients a, b, and c
- Quickly determines the discriminant to check root nature
Examples
- Solve the equation 2x² - 4x - 6 = 0: The discriminant is 64, leading to solutions x₁ = 3 and x₂ = -1.
Common Use Cases
- Students solving algebra homework problems involving quadratic equations
- Teachers preparing examples for lessons on quadratic functions
- Engineers and scientists modeling physical phenomena with quadratic relationships
- Anyone needing to quickly determine roots and their type for quadratic equations
Tips & Best Practices
- Double-check that your equation is in the standard quadratic form before inputting values
- Use accurate coefficient values to ensure precise calculation results
- Interpret the discriminant to understand whether solutions are real or complex
- Reconfirm results especially when dealing with complex roots
Limitations
- Only solves equations strictly in the form ax² + bx + c = 0
- Does not support higher-degree polynomial equations
- Cannot solve systems of equations involving multiple variables
Frequently Asked Questions
- What type of equations can this calculator solve?
- It solves quadratic equations of the form ax² + bx + c = 0 using the quadratic formula.
- Can this tool handle complex roots?
- Yes, it accurately computes both real and complex solutions by evaluating the discriminant.
- Does this calculator work for equations with degree higher than two?
- No, it is limited to standard quadratic equations and does not process higher-degree polynomials.
Key Terminology
- a
- The coefficient of the term x squared (x²) in the quadratic equation.
- b
- The coefficient of the term x in the quadratic equation.
- c
- The constant term in the quadratic equation.
- x
- The solution(s) or root(s) of the quadratic equation.
- Discriminant
- The expression b² - 4ac used to determine the nature of the roots.