Fundamental theorem of algebra

High school (ages 12+)
Mathematics & Numbers

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Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/fundamental-theorem-of-algebra

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the mathematical property?The field of complex numbers is algebraically closed
2. What is the number of roots (with multiplicity)?A polynomial of degree n has exactly n complex roots
3. Why does every polynomial have a root?Because the set of complex numbers is algebraically closed, so you never need to look outside that set to solve polynomial equations.
4. How many roots does a polynomial of degree n have?It has exactly n complex roots, counting multiplicity. If a root appears twice, it counts as two roots.

Algebraically Closed Field: A number system where every polynomial equation has a solution within that system.
Complex Coefficients: Numbers of the form a + bi, where 'a' and 'b' are real numbers and 'i' is the imaginary unit.
Successive Polynomial Division: A method of repeatedly dividing a polynomial by factors corresponding to its roots to find all roots.