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. −x^2+2x≥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.

Graphing on a Number Line

Graphing the solution set of an inequality on a number line visually represents the range of values that satisfy the inequality. Solutions are typically indicated with open or closed circles to denote whether endpoints are included (closed) or excluded (open), and shaded regions show the intervals of valid solutions.

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 or excluded. For example, (a, b) means all numbers between a and b, excluding a and b, while [a, b] includes both endpoints.