All You Need to Know About Finding the Zeros of Polinomial Equations

🔍The complex conjugate root theorem states that if a+bi is a root, then a-bi is also a root.

📈Finding all the zeros of a polinomial equation involves factoring and using long division.

💡The fundamental theorem of algebra guarantees that every polinomial with a degree greater than one has at least one complex zero.

🔄To determine the zeros of a polinomial equation, set each factor equal to zero and solve for x.

🧮Practice problem-solving skills by working through examples and applying the complex conjugate root theorem.

What is the complex conjugate root theorem?

—The complex conjugate root theorem states that if a+bi is a root of a polinomial equation, then a-bi is also a root.

How do you find the zeros of a polinomial equation?

—To find the zeros, set each factor equal to zero and solve for x.

What is the fundamental theorem of algebra?

—The fundamental theorem of algebra guarantees that every polinomial with a degree greater than one has at least one complex zero.

What is the process of factoring a polinomial equation?

—Factoring involves finding the factors of the equation and breaking it down into simpler terms.

When should long division be used to find the zeros of a polinomial equation?

—Long division is used when the equation cannot be easily factored.

00:18Introduction to finding the zeros of polinomial equations using the complex conjugate root theorem.

01:10Explanation of the complex conjugate root theorem and how it relates to finding all the zeros of a polinomial equation.

03:23Demonstration of an example problem and the step-by-step process of finding the zeros using the complex conjugate root theorem.

06:25Discussion on the fundamental theorem of algebra and its relevance to finding the zeros of a polinomial equation.

08:40Explanation of factoring and long division as methods to determine the zeros of a polinomial equation.