Mathway Quadratic Formula Calculator
Solve quadratic equations using the quadratic formula. Enter coefficients a, b, and c to get real or complex roots with step-by-step explanation.
Published by:
isCalculator Editorial Team
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How to use this tool?
How to Use the Quadratic Formula Calculator
- Enter coefficients – Input numeric values for a, b, and c from the equation ax² + bx + c = 0. The a coefficient cannot be zero.
- Click "Calculate" – The calculator validates your inputs and shows errors if any field is missing or invalid.
- Read the result – The solution displays as:
- Two distinct real roots (if discriminant > 0)
- One repeated real root (if discriminant = 0)
- Two complex conjugate roots (if discriminant < 0)
- Review steps – Below the result, a step-by-step breakdown shows the discriminant calculation and the formula applied.
Tip: Use decimal numbers (e.g., 2.5) or fractions (e.g., 0.333) as needed. The calculator rounds results to 4 decimal places.
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Frequently Asked Questions
The quadratic formula is x = [-b ± √(b² - 4ac)] / (2a) for solving quadratic equations of the form ax² + bx + c = 0.
The discriminant (b² - 4ac) determines the nature of the roots: positive means two distinct real roots, zero means one real repeated root, negative means two complex roots.
Yes, as long as the equation is in the form ax² + bx + c = 0 with a ≠ 0. Enter the coefficients a, b, and c.
