A quadratic inequality asks when a quadratic expression is greater than, less than, or equal to zero. To solve one, first find the boundary values by solving the related quadratic equation where the expression equals zero.

The roots split the number line into regions. For an upward-opening parabola, the expression is positive outside the roots and negative between them.

Strict signs $<$ and $>$ do not include the roots. Inclusive signs $\le$ and $\ge$ do include them.