Quadratic Formula Calculator
Solve quadratic equations of the form ax² + bx + c = 0 using the quadratic formula. Get real or complex roots, step-by-step solution, and discriminant analysis.
Published by:
isCalculator Editorial Team
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How to use this tool?
This calculator solves quadratic equations of the form ax² + bx + c = 0 using the quadratic formula. Follow these steps:
- Enter coefficients a, b, and c in the input fields. Use numbers (decimals allowed).
- Click "Calculate Roots" to see the results.
- Review the output:
- Roots: The solutions for x (real or complex).
- Discriminant (Δ = b² - 4ac): Indicates root type:
- Δ > 0 → two distinct real roots
- Δ = 0 → one real repeated root
- Δ < 0 → two complex conjugate roots
- Steps: Shows the calculation process.
- Note: Coefficient a cannot be zero (otherwise it's not quadratic).
All inputs are in the same unit system (no conversion needed). Results are rounded to 4 decimal places.
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Frequently Asked Questions
The quadratic formula is x = [-b ± √(b² - 4ac)] / (2a) for solving quadratic equations ax² + bx + c = 0.
The discriminant Δ = b² - 4ac determines the nature of roots: Δ > 0 gives two distinct real roots, Δ = 0 gives one real repeated root, Δ < 0 gives two complex roots.
No, if a = 0 the equation is linear, not quadratic. The calculator will show an error.
