Quadratic Inequality Calculator (Free, Step-by-Step)

Use this free quadratic inequality calculator to solve inequalities like ax² + bx + c > 0. It finds the roots, determines where the inequality holds, and gives the solution in interval notation with a shaded graph.

How to solve a quadratic inequality

Find the roots of the related equation, then test the sign of the parabola on each interval. An upward parabola is positive outside its roots and negative between them (and vice versa).

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How to use it

1. Enter a, b, c and pick the inequality sign.
2. Press Solve.

Related: the Inequality Calculator and more free math calculators.

Frequently asked questions

What if there are no real roots?

Then the parabola keeps one sign everywhere, so the solution is either all real numbers or no solution.

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Do ≥ and ≤ include the roots?

Yes — the calculator uses closed brackets for ≥ and ≤ and open ones for > and <.

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Is the answer in interval notation?

Yes, with a number-line style shaded graph.

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