Solve each quadratic inequality. Give the solution set in interval notation. See Exam-ples 5 and 6. 2x^2-9x≤18

Key Concepts

Quadratic Inequalities

Quadratic inequalities are expressions that involve a quadratic polynomial set in relation to a value using inequality symbols (e.g., ≤, ≥, <, >). To solve these inequalities, one typically finds the roots of the corresponding quadratic equation and then tests intervals to determine where the inequality holds true.

Interval Notation

Interval notation is a mathematical notation used to represent a range of values. It uses parentheses and brackets to indicate whether endpoints are included (closed interval) or excluded (open interval). For example, (a, b) represents all numbers between a and b, not including a and b, while [a, b] includes both endpoints.

Factoring Quadratics

Factoring quadratics involves rewriting a quadratic expression as a product of its linear factors. This is essential for solving quadratic equations and inequalities, as it allows one to find the roots easily. For example, the quadratic expression ax^2 + bx + c can often be factored into (px + q)(rx + s), where p, q, r, and s are constants.