Quadratic Equation Calculator
Solve ax² + bx + c = 0, including real, repeated and complex roots. Inspect the discriminant, worked steps and the function graph.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Calculate the discriminant D = b² − 4ac. Positive D gives two real roots; zero gives a repeated root; negative D gives a complex-conjugate pair. The graph displays the real function, so complex roots are not real x-intercepts. If a is zero, solve the remaining linear equation.
x = (−b ± √(b² − 4ac))/(2a)
Worked example
For x² − 5x + 6 = 0, D = 25 − 24 = 1. The roots are (5 − 1)/2 = 2 and (5 + 1)/2 = 3. The vertex is (2.5, −0.25).
Assumptions and input details
Coefficients may be negative or zero. The all-zero equation has infinitely many solutions. A nonzero constant equal to zero has no solution. Numeric outputs use floating-point arithmetic.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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