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: - RoadRUNNER Motorcycle Touring & Travel Magazine

Understanding the Context

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.

Here, the root $ x = 1 $ has multiplicity 2, while $ x = -2 $ appears once.

Total Number of Distinct Real Roots

The distinct real roots are simply the unique values where the polynomial equals zero. From the given roots:

• $ x = 1 $
  
• $ x = -2 $

Key Insights

There are two distinct real roots.

Total Real Roots Counting Multiplicity

When counting real roots including multiplicity, we sum up how many times each root appears.

• $ x = 1 $ contributes 2
  
• $ x = -2 $ contributes 1

Adding:
2 + 1 = 3 real roots counting multiplicity

Why This Distinction Matters

Final Thoughts

Although there are only two distinct x-values where the function crosses or touches the x-axis, counting multiplicity gives a more complete picture of the function’s behavior. This distinction is valuable in applications such as stability analysis in engineering or modeling growth with repeated influence points.

Summary

| Property | Value |
|--------------------------------|--------------|
| Distinct real roots | 2 ($ x = 1 $, $ x = -2 $) |
| Real roots counting multiplicity | 3 (due to double root at $ x = 1 $) |

Answer: There are two distinct real roots, but three real roots counting multiplicity.

This clear separation between distinct and counted roots enhances polynomial analysis and supports deeper insights into the nature of solutions. Whether solving equations or modeling real-world phenomena, recognizing multiplicity ensures accurate interpretation.