A quadratic equation asks where the parabola touches the ground — a quadratic inequality asks where it flies above or burrows below. Solving x² − 5x + 6 > 0 means finding every x where the parabola sits above the x-axis, and the answer is a region (or regions), not points: x < 2 or x > 3, the two outer stretches where the upward-opening parabola rides high. Business students meet this as "for which quantities is profit positive?" — the break-even points are the roots, and the profitable zone is the inequality's solution.

The sign-chart method is the reliable path: find the roots (the boundary points), plot them on a number line, and test one value in each region. The parabola's shape does half the work — an upward-opening parabola (positive a) is positive outside its roots and negative between them; flip that for downward-opening. Boundary inclusion follows the symbol: > and < exclude the roots (open circles), ≥ and ≤ include them (closed dots). This calculator checks your quadratic inequality work: enter the two key values and confirm the computed result. Always finish with a test point from your claimed solution — x = 0 in x² − 5x + 6 gives 6 > 0, true — because sign errors are silent and the test point catches them.

With the pre-filled defaults — Variable A 10, Variable B 5 — the Quadratic Inequality Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.