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Chapter 6.13
Fundamental theorem of algebra
What You'll Learn
State the fundamental theorem of algebra: a degree n polynomial has exactly n roots
Distinguish between real roots and imaginary roots in polynomial equations
Recognize that imaginary roots always occur in conjugate pairs
Factor polynomials into linear factors and irreducible quadratic factors
Understand multiplicity and how repeated roots affect polynomial graphs
Determine all possible combinations of real and imaginary roots for any polynomial
What You'll Practice
1
Finding all roots of degree 3 and higher polynomials using factoring techniques
2
Applying the quadratic formula to irreducible quadratic factors
3
Counting real and imaginary roots including multiplicity
4
Listing possible root combinations for polynomials of varying degrees
Why This Matters
The fundamental theorem of algebra is essential for understanding polynomial behavior in calculus, engineering, and physics. It guarantees that every polynomial equation has solutions and helps you predict how many x-intercepts a function will have, which is critical for graphing, optimization, and solving real-world problems.
Before You Start — Make Sure You Can:
This Unit Includes
3 Video lessons
Practice exercises
Skills
Polynomial Roots
Fundamental Theorem of Algebra
Imaginary Numbers
Factoring
Multiplicity
Quadratic Formula
Irreducible Quadratics
Complex Conjugates
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