Algebraic equations with one unknown. Ruffini's rule

In this video, the presenter explains the concept of algebraic equations with a single unknown and how to solve such equations using various methods including the rule of Ruffini. Initially, the basics of algebraic equations are defined, their degree is determined by the highest power of the unknown, and their coefficients and constants are identified. Examples illustrate equations from degree 1, which are straightforward to solve, to degree 2, where solving involves a quadratic formula that can yield real or complex solutions depending on the discriminant (b^2 - 4ac). For higher-degree equations, the discussion shifts to biquadratic equations, where substitution can reduce the problem to a quadratic one. The process of Ruffini's rule is detailed using a step-by-step approach to evaluate potential solutions of higher-order algebraic equations. This technique is used to iteratively determine whether a number is a root of the equation and to factor the polynomial accordingly. The video provides clear examples to demonstrate the application of these methods, including finding complex solutions and identifying multiplicity in roots. The video concludes with an emphasis on the methods and rationale behind solving various types of algebraic equations, from linear and quadratic to higher-order polynomials, showcasing the Ruffini rule as a critical tool for tackling more complex equations.