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Inequality Calculator

Solve real linear or quadratic inequalities in the form ax² + bx + c compared with zero. See critical points, interval notation and a number-line summary.

Supports only constant, linear and quadratic real inequalities ax² + bx + c <, ≤, > or ≥ 0. Coefficients must be finite, with absolute values at most 10⁹. Roots are approximate because calculations use floating-point numbers. A scale-based tolerance is used near repeated roots.

How do you solve a quadratic inequality?

Find the real zeros of the polynomial, then determine its sign between and outside those zeros. This tool returns the real solution intervals and whether each finite endpoint is included.

Frequently asked questions

How do you solve a quadratic inequality?

Find the real zeros of the polynomial, then determine its sign between and outside those zeros. This tool returns the real solution intervals and whether each finite endpoint is included.

Are my coefficients uploaded?

No. The inequality is calculated in this browser and is not uploaded or saved by this tool.

What does interval notation show?

Parentheses mean an endpoint is excluded, while square brackets mean it is included. Infinity always uses parentheses because infinity is not a real endpoint.

Can I solve cubic or rational inequalities?

No. This calculator is limited to real polynomials of degree zero, one or two. It does not solve cubic, rational, absolute-value or compound inequalities.

Are the roots exact?

No. Coefficients and roots use floating-point arithmetic. Results near repeated roots or with very different coefficient sizes can be sensitive to rounding.