Name: ECUACIONES DE 2° GRADO (MÉTODO DE FACTORIZACIÓN)
Uploaded: 2023-09-03T23:00:09.000Z
Duration: 20 min 7 s
Description: Ejemplos resueltos de Ecuaciones de 2° Grado utilizando el Método de Factorización.

ECUACIONES DE 2° GRADO (MÉTODO DE FACTORIZACIÓN)

Introduction to Quadratic Equations

Overview of Quadratic Equations

The speaker, Licenciado Bolívar, introduces the topic of quadratic equations in the form ax^2 + bx + c = 0 , emphasizing that a must be non-zero.

The discussion begins with a question about methods for solving quadratic equations, highlighting four main approaches: factorization, completing the square, and the general formula (also known as Bhaskara's formula).

Methods for Solving Quadratic Equations

An interesting method proposed by Professor Pochen is mentioned, which utilizes properties of roots to construct solutions.

Factorization Method

Example 1: Solving x^2 - 3 = 0

The first example involves solving x^2 - 3 = 0 . The theorem states that if x^2 = a for any non-negative real number a , then x = pmsqrta .

Applying this theorem leads to immediate results: x = pmsqrt3 , thus the solution set is expressed as sqrt3, -sqrt3 .

Difference of Squares

Another approach using the difference of squares is introduced. It states that A^2 - B^2 = (A-B)(A+B) .

For this equation, it can be rewritten as (x - sqrt3)(x + sqrt3) = 0, leading to two potential solutions.

Second Example: Factoring Common Terms

Example 2: Solving y - 2y^2 = 0

In this case, common terms are factored out from the equation. The expression simplifies to y(2y - 1) = 0.

This results in two solutions: either y = 0 or solving for when 2y - 1 = 0, yielding another solution at y = 1/2.

Third Example: Simple Cross Factorization

Example 3: Using Simple Cross Factorization

The third example employs simple cross factorization. It requires decomposing both the quadratic term and constant term into factors.

By ensuring these factors yield both correct products and sums corresponding to their respective coefficients, successful factorization transforms the quadratic expression into linear factors.

Solving Equations: Finding Solutions

Analyzing the Equation

The discussion begins with a horizontal reading of the equation, specifically focusing on two terms: 2t - 1 and t - 2.

It is noted that the product of these terms equals zero, leading to the conclusion that either 2t - 1 = 0 or t - 2 = 0.

Solving for T, it is determined that T = 1/2 from the first equation and T = 2 from the second.