How do you show an equation has 3 real roots?

To show that an equation has three real roots, you can analyze its derivative to find critical points and determine the behavior of the function. If the function is continuous and differentiable, use the Intermediate Value Theorem to confirm sign changes between critical points, indicating the presence of roots. Additionally, applying Descartes' Rule of Signs can help estimate the number of positive and negative roots. Finally, plotting the function or using numerical methods can provide visual confirmation of the three real roots.