Complex Solutions and Factoring Techniques

The video tutorial explains how to find all four complex solutions to the equation x^4 = 16. It begins by highlighting the limitations of using the fourth root method, which only provides two solutions. The tutorial then demonstrates how to factor the equation to find all solutions, including real solutions x = 2 and x = -2, and complex solutions involving imaginary numbers. The process involves setting each factor to zero and solving for x, ultimately yielding the complete set of solutions.

What is the limitation of taking the fourth root of both sides of the equation x^4 = 16?

• It only provides two solutions.

• It results in no solutions.

• It provides three solutions.

• It gives all four solutions.

What is the first step in solving the equation by factoring?

• Divide both sides by 4.

• Multiply both sides by 4.

• Add 16 to both sides.

• Subtract 16 from both sides.

Which of the following is a real solution obtained from factoring the equation?

• x = 3

• x = 2

• x = -3

• x = 4

How do you find the complex solutions after factoring?

• By setting x^2 - 4 equal to zero.

• By setting x^2 + 4 equal to zero.

• By setting x^2 - 16 equal to zero.

• By setting x^2 + 16 equal to zero.

What are the complex solutions to the equation x^2 + 4 = 0?

• x = ±2

• x = ±4i

• x = ±2i

• x = ±i