Solve each quadratic inequality. Give the solution set in interval notation. See Exam-ples 5 and 6. x^2-7x+10>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 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 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 Points

Test points are specific values chosen from the intervals created by the roots of a quadratic inequality. By substituting these points back into the inequality, one can determine whether the inequality is satisfied in that interval. This method is essential for identifying the solution set in interval notation.