Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. 3x^2−5x≤0

Key Concepts

Polynomial Inequalities

Polynomial inequalities involve expressions that compare a polynomial to a value, typically zero, using inequality symbols such as ≤, ≥, <, or >. To solve these inequalities, one must find the values of the variable that make the inequality true, often by determining the roots of the polynomial and testing intervals between these roots.

Interval Notation

Interval notation is a mathematical notation used to represent a range of values on the real number line. It uses parentheses and brackets to indicate whether endpoints are included (closed intervals) or excluded (open intervals). For example, the interval [a, b) includes 'a' but not 'b', while (a, b) excludes both endpoints.

Graphing Solution Sets

Graphing solution sets on a real number line visually represents the values that satisfy the inequality. This involves marking the critical points (roots) and shading the appropriate regions based on the inequality's direction. Understanding how to accurately depict these solutions helps in interpreting the results of polynomial inequalities.