The roots are $ x = 1 $ (with multiplicity 2) and $ x = -2 $. Therefore, there are **two distinct real roots**, but **three real roots counting multiplicity**. Since the question asks for the number of real roots (not distinct), the answer is:

Mon, 04 May 2026 06:24:05 +0000

Understanding the Real Roots of the Polynomial: Analyzing $ x = 1 $ (Multiplicity 2) and $ x = -2 $ When solving polynomial equations, understanding both the number of distinct real roots and the total real roots counting multiplicity is essential for accurate interpretation. In the case of the polynomial with roots $ x = 1 $ (with multiplicity 2) and $ x = -2 $, let’s break down how these roots shape the overall structure of the equation and its real solutions. ### What Does Multiplicity Mean? Multiplicity refers to the number of times a particular root appears in a polynomial. A root with multiplicity 2 (or higher) means that the graph of the polynomial touches but does not cross the x-axis at that point—instead, it “bounces” off. A simple root (multiplicity 1) results in a clear crossing of the x-axis.