Математика15 мин

Quadratic Inequalities

Sign analysis on a parabola — find roots, then test intervals.

Three-step method

Open-up parabolas are negative **between** their roots and positive **outside**. Open-down is the reverse.

Solve

Solve $x^2 - 5x + 6 < 0$ .

Жауап: $2 < x < 3$

Жаттығу

Solve $x^2 - 9 \ge 0$ .

Жауап пен түсініктемені көру

Жауап: $x \le -3$ or $x \ge 3$

$(x-3)(x+3) \ge 0$ . Roots at $\pm 3$ , parabola up. Non-negative outside.