Understanding Polynomial Equations

The video tutorial explains how to find the zeros of a degree four polynomial equation by recognizing its quadratic form. It uses substitution to transform the equation into a quadratic, which is then factored. The solutions are found using square roots, resulting in two imaginary and two irrational solutions. The solutions are verified using a calculator.

What is the degree of the polynomial equation discussed in the video?

• Three

• Four

• Two

• Five

What substitution is made to transform the degree four polynomial into a quadratic form?

• u = x^3

• u = x^4

• u = x

• u = x^2

What are the factors of the quadratic equation after substitution?

• u + 9 and u + 2

• u - 9 and u + 2

• u + 9 and u - 2

• u - 9 and u - 2

What is the next step after factoring the quadratic equation?

• Substitute back to x

• Multiply the factors

• Solve for u

• Add the factors

What is the result of solving x^2 + 9 = 0?

• x = ±3

• x = ±3i

• x = ±√2

• x = ±√9

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

• x = ±3i

• x = ±3

• x = ±√2

• x = ±2

How many imaginary solutions are found for the polynomial equation?

• Three

• Two

• Four

• One

How many irrational solutions are found for the polynomial equation?

• One

• Four

• Two

• Three

Which of the following is an imaginary solution to the equation?

• 2

• 3i

• √2

• 3

Which of the following is an irrational solution to the equation?

• 9

• √2

• 2

• 3i