Linear and Quadratic Inequality Calculator
Solve a linear or quadratic inequality against zero. See the solution intervals, open or closed endpoints, a sign chart and a number line.
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
Find the real zeros, then determine the sign on each interval between them. Keep intervals with the required sign. Include the zeros only for ≤ or ≥, and merge intervals that meet at an included endpoint.
Solve f(x) <, ≤, > or ≥ 0 by combining its zeros with the signs between those zeros.
Worked example
x²−5x+6=(x−2)(x−3). It is negative between 2 and 3, so x²−5x+6≤0 gives [2,3], while the strict inequality gives (2,3). For −2x+4>0, dividing by −2 reverses the sign and gives x<2.
Assumptions and input details
Coefficients must be integers within ±1e6. Set a=0 to reduce a quadratic expression to a linear or constant one. In linear mode the hidden a field is ignored. Endpoints at irrational roots are rounded decimal approximations; the discriminant uses exact integer-valued arithmetic within these bounds. Parentheses exclude an endpoint and square brackets include it; infinity is never included. A repeated root can give one point, all real numbers, all except that point, or no solution, depending on the relation.
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.
Solve ax+b=cx+d with whole numbers, decimals or fractions. Follow the same operation on both sides and check the answer by substitution.
Solve ax² + bx + c = 0, including real, repeated and complex roots. Inspect the discriminant, worked steps and the function graph.
Find the maximum and minimum of ax²+bx+c on an entered closed interval. Compare both endpoints and the vertex, with a graph and candidate table.
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