Test
Quadratic inequalities
This test develops methods for solving quadratic inequalities using roots and the sign of a parabola. Tasks cover selecting intervals, handling strict and non-strict boundaries and writing the solution in interval notation.
Time left: 00:00:00
Sample questions
- Solve (x − (___))(x − (___)) > 0.
- Solve (x − (___))(x − (___)) < 0.
- Solve (x − (___))(x − (___)) ≤ 0.
- Solve x² < ___.
- Solve x² > ___.
Quadratic inequalities
Solve a quadratic inequality by analysing the sign of ax² + bx + c. First find its zeros, mark them on a number line and determine the sign on every resulting interval.
Parabola method
For a > 0, the parabola is above the x-axis outside two roots and below it between them; for a < 0, the signs reverse. The symbols ≤ and ≥ include roots, while < and > exclude them. With no real roots, the expression has the sign of a everywhere.
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