Quadratic inequality solver
Enter the coefficients and choose the sign to see which x values satisfy the inequality.
Loading the tool…
Processing and privacy: The result is calculated inside your browser and your data is not sent to any server.
How to use it
- Enter coefficient a, coefficient b, coefficient c and sign compared with 0.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Find the roots of ax² + bx + c = 0. For a > 0 the expression is positive outside the roots and negative between them; the signs reverse for a < 0. With no real roots it always has the sign of a.
Example
Inputs: Coefficient a = 1, Coefficient b = -4, Coefficient c = 3, Sign compared with 0 = greater than (>). Result: Solution: x < 1 or x > 3; Roots of the related equation: x = 1, x = 3.
Limits and caveats
- The right side must be 0; move every term to the left first.
- Irrational roots appear as rounded decimals.
Questions about this tool
How do I solve x² > 9?
Write it as x² - 9 > 0: a = 1, b = 0, c = -9. The answer is x < -3 or x > 3.
Why is the answer sometimes two intervals?
An upward parabola is above the x axis left of the smaller root and right of the larger one.
What does ∪ mean?
Union: x belongs to the first interval or the second.