The primary aim of this experiment is to determine the roots of algebraic and transcendental equations using systematic numerical methods.

Algebraic equations involve polynomial expressions, and their solutions (roots) can often be found exactly or approximately, depending on the degree of the equation. In contrast, transcendental equations involve functions such as exponential, logarithmic, or trigonometric functions, which generally do not have closed-form solutions and thus require iterative or approximation techniques.

Through this experiment, the objective is not only to compute the roots but also to understand:

1. The nature and behavior of algebraic equations, including how balance and symmetry play roles in their solution.
2. The complexity of transcendental equations, which often demand numerical approaches like Newton-Raphson or Bisection methods for finding approximate solutions.
3. The importance of roots in mathematics and applied sciences, as they appear in problems of physics, engineering, economics, and computer science.

By performing this experiment, students will gain deeper insight into the differences between algebraic and transcendental equations, develop problem-solving skills using both analytical and numerical approaches, and appreciate the role of computational techniques in solving real-world mathematical problems.