Quadratic Equation Solver (ax² + bx + c = 0)
Local ProcessingSolve quadratic equations ax² + bx + c = 0 using the quadratic formula, computing real and complex roots.
How It Works & Processing Standards
Enter values above to calculate results automatically. Check each input field for guidance and units.
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Choose roots or discriminant only under "Calculation". The sign of D = b² − 4ac tells you the kind of roots.
What You Can Do
- Roots
- x = (−b ± √D) ÷ 2a, labeled as two real roots, a double root or complex roots.
- Discriminant only
- D = b² − 4ac: positive means two real roots, 0 a double root, negative complex roots.
How to Use Quadratic Equation Solver (ax² + bx + c = 0)
- 1Choose a calculationRoots, or discriminant only to see the kind of roots.
- 2Enter coefficientsa (not 0), b and c.
- 3Read the resultBoth roots and the discriminant.
Examples
x² − 5x + 6 = 0
Input: a 1, b −5, c 6
Result: x₁ = 3, x₂ = 2
Discriminant of x² + 2x + 5
Input: a 1, b 2, c 5 (discriminant)
Result: -16
Common Use Cases
- Checking school math homework
- Where a parabola crosses the x-axis
- Solving quadratics in physics problems
Frequently Asked Questions (FAQ)
What if a is 0?
It is no longer quadratic, so you are told to check the input.
How are complex roots shown?
As real and imaginary parts.