Quadratic Form and Solving Equations

The video tutorial explains how to solve a degree 4 equation by recognizing it as a quadratic form. It introduces a substitution method using a new variable, u, to convert the equation into a quadratic equation. The tutorial then demonstrates factoring the equation in terms of u and solving for x by taking square roots. Finally, it verifies the solutions by substituting them back into the original equation, confirming four possible solutions: x equals plus or minus four, and plus or minus two.

Why is the given equation considered to be in quadratic form?

• Because it can be rewritten using a substitution.

• Because it has a degree of 2.

• Because it is already a quadratic equation.

• Because it has no solutions.

What substitution is made to transform the equation into a quadratic form?

• Let u equal x.

• Let u equal x to the fourth.

• Let u equal x cubed.

• Let u equal x squared.

What are the factors of the quadratic equation in terms of u?

• u - 16 and u - 4

• u + 16 and u + 4

• u + 16 and u - 4

• u - 16 and u + 4

After substituting back to x, what are the factors of the original equation?

• x squared minus 16 and x squared plus 4

• x squared minus 16 and x squared minus 4

• x squared plus 16 and x squared minus 4

• x squared plus 16 and x squared plus 4

What are the solutions for x when x squared equals 16?

• x equals plus or minus 8

• x equals plus or minus 4

• x equals plus or minus 2

• x equals plus or minus 1

What are the solutions for x when x squared equals 4?

• x equals plus or minus 8

• x equals plus or minus 4

• x equals plus or minus 2

• x equals plus or minus 1

How many solutions does the original equation have?

• Two solutions

• Four solutions

• Three solutions

• No solutions

Which of the following is a correct solution for the original equation?

• x equals 0

• x equals plus or minus 4

• x equals plus or minus 3

• x equals plus or minus 5

What is the purpose of verifying the solutions by substituting back into the original equation?

• To ensure the solutions satisfy the original equation

• To find new solutions

• To change the solutions

• To eliminate incorrect solutions

What is the result of substituting x equals 4 back into the original equation?

• The equation equals four

• The equation equals zero

• The equation is not satisfied

• The equation equals one