Quadratic Inequality Solver
Enter the coefficients of a quadratic inequality ax² + bx + c OP 0. The solver computes the discriminant, finds the roots, reasons about the sign of the parabola via its sign chart and returns the solution set in interval notation.
Frequently asked questions
How is the sign chart built?
A parabola with positive leading coefficient is positive outside its roots and negative between them; with a negative leading coefficient the signs flip. The solver applies this rule to the inequality direction you chose.
What if the discriminant is negative?
The quadratic never crosses zero, so it keeps the sign of its leading coefficient everywhere. The solution is therefore either all real x or no real x, depending on the chosen inequality.
What about a repeated root?
When Δ = 0 the quadratic touches zero at a single point. The solver reports either that single point, the complement of it, all real x or no solution depending on the inequality.