Solving Quadratic Equations and Factorization

The video tutorial explains how to solve a fourth-order algebraic equation using the factorization method. The equation is expressed as X^4 - 4X^2 - 6^2 + 4 = 0, which is then factorized into two parts: (X^2 - 4) and (X^2 - 1). Solving these factors results in four roots: X = ±2 and X = ±1. The tutorial guides viewers through each step, ensuring a clear understanding of the process.

What is the expected number of roots for a fourth order algebraic equation?

• Five

• Four

• Three

• Two

Which method is used to solve the fourth order equation in the video?

• Graphical Method

• Substitution Method

• Factorization Method

• Numerical Method

What is the first step in solving the fourth order equation using factorization?

• Finding the derivative

• Expressing it as a product of factors

• Using the quadratic formula

• Graphing the equation

How is the fourth order equation expressed in the factorization method?

• As a sum of squares

• As a product of linear factors

• As a difference of squares

• As a product of quadratic factors

What are the two factors obtained from the factorization of the equation?

• x^2 - 4 and x^2 + 1

• x^2 + 4 and x^2 - 1

• x^2 - 4 and x^2 - 1

• x^2 + 4 and x^2 + 1

Which of the following is a correct factorization of x^4 - 4x^2 - 6x + 4?

• (x^2 - 2)(x^2 - 3)

• (x^2 + 2)(x^2 - 1)

• (x^2 + 4)(x^2 + 1)

• (x^2 - 4)(x^2 - 1)

What is the solution for x when x^2 - 4 = 0?

• x = 0

• x = ±1

• x = ±3

• x = ±2

What is the solution for x when x^2 - 1 = 0?

• x = ±1

• x = ±3

• x = 0

• x = ±2

What is the result of solving x^2 - 4 = 0?

• x = ±4

• x = ±3

• x = ±2

• x = ±1

What is the result of solving x^2 - 1 = 0?

• x = ±2

• x = ±1

• x = ±4

• x = ±3