About This Chapter
Roots & Coefficients of Polynomials - Chapter Summary
Work through this chapter at your own pace to review the roots and coefficients of polynomials. These simple lessons are designed to help you improve your understanding of the rational roots theorem, the intervals of polynomial functions and polynomial coefficients. You'll also see how Newton's method can be used to find the roots of equations. By the end of the chapter, you'll be able to:
- Understand the roots and coefficients of polynomials
- Comprehend the rational roots theorem
- Evaluate multiple roots of polynomials
- Form polynomial equations with various types of roots
- Identify polynomial function intervals
- Find equation roots using Newton's method
In addition to the lessons, this chapter includes interactive self-assessment quizzes to help you strengthen your problem-solving abilities. Our instructors are available to answer any questions you may have about the lesson material. You can access the chapter on any computer or mobile device, which allows you to study wherever and whenever it's convenient.
1. How to Use the Rational Roots Theorem: Process & Examples
When it comes to solving polynomials, it can sometimes be easier to begin with a list of possible solutions to try. This video lesson tells you how to form a list of possible solutions by using the rational roots theorem.
2. Multiple Roots of Polynomials
This lesson will review the definitions of polynomials and roots of polynomials. We will then look at multiple roots of polynomials and learn some tricks on how to determine a lot about a polynomial by just looking at it in its completely factored form.
3. Forming Polynomial Equations with Roots
In this lesson you'll learn how to form polynomial equations when given the roots of the equation and look at some examples. Sample problems will include those involving multiple roots and squares.
4. Finding Intervals of Polynomial Functions
Watch this video lesson to learn how you can find the intervals of a polynomial function. Also learn how to find out whether each interval is negative or positive.
5. How to Use Newton's Method to Find Roots of Equations
Finding the roots of equations usually requires the use of a calculator. However, in this lesson you'll use Newton's Method to find the root of any equation, even when you can't solve for it explicitly.
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Other chapters within the HSC Mathematics: Exam Prep & Syllabus course
- Mathematical Proofs & Reasoning
- Basic Arithmetic & Algebra
- Factorization of Binomials & Trinomials
- Types of Equations & Inequalities
- Plane Geometry
- Circle Plane Geometry
- Probability & Randomization
- Arithmetic & Geometric Series
- Trigonometric Ratios
- Geometrical Representations of Functions
- Linear Functions & Lines
- Derivatives of Functions
- Quadratic Polynomials & Parabolas
- Geometrical Applications of Differentiation
- Logarithmic & Exponential Functions
- Calculating Trigonometric Functions
- Understanding Inverse Functions
- Factoring & Graphing Polynomials
- Binomial Theorem & Probability
- Graphing & Solving Functions
- Solving & Graphing Complex Numbers
- Geometric Representations of Complex Numbers
- Square Roots, Powers & Roots of Complex Numbers
- Conic Sections Basics
- The Ellipse in Algebra
- The Hyperbola
- The Rectangular Hyperbola
- Calculus Applications: Rate of Change
- Calculus Applications: Velocity & Acceleration
- Calculus Applications: Projectile & Harmonic Motion
- Calculus Applications: Resisted Motion
- Calculus Applications: Circular Motion
- HSC Mathematics Flashcards