Solve each quadratic inequality. Give the solution set in interval notation. See Exam-ples 5 and 6. x^2-x-6>0

Key Concepts

Quadratic Inequalities

Quadratic inequalities are expressions that involve a quadratic polynomial set in relation to zero, typically in the form ax^2 + bx + c > 0, < 0, ≥ 0, or ≤ 0. To solve these inequalities, one must first find the roots of the corresponding quadratic equation, which helps determine the intervals to test for the inequality's truth.

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 intervals) or excluded (open intervals). For example, (a, b) represents all numbers between a and b, not including a and b, while [a, b] includes both endpoints.

Test Intervals

After determining the roots of the quadratic inequality, the real number line is divided into intervals based on these roots. To find where the inequality holds true, one selects test points from each interval and substitutes them back into the inequality. The results indicate whether the entire interval satisfies the inequality, allowing for the construction of the solution set.