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Solving polynomial equations by iteration

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Grade 11 Pre-Calculus Mathematics (30S)
Develop algebraic and graphical reasoning through the study of relations
13. Solve problems involving quadratic equations
13.6 Solving polynomial equations by iteration

Mastering Polynomial Equations with Iteration Formulas

Unlock the power of iteration formulas to solve complex polynomial equations. Learn direct iteration, bisection, and Newton-Raphson methods to tackle challenging math problems with confidence and precision.

What You'll Learn

Define iteration as a method to refine approximate solutions by repeating calculations
Apply direct iteration by rearranging equations and substituting results repeatedly
Use bisection iteration to narrow solution intervals by dividing regions in half
Calculate solutions using the Newton-Raphson formula with derivatives
Determine when to stop iterating based on desired accuracy or consistent answers

What You'll Practice

1

Rearranging polynomial equations into iteration formula form

2

Performing direct iteration with quadratic and cubic functions

3

Creating tables to track bisection iteration steps and intervals

4

Using calculators to speed up repeated iterations

5

Applying Newton-Raphson method with derivatives to approximate roots

Why This Matters

Iteration methods let you solve complex polynomial equations that don't factor easily, giving you powerful numerical techniques used in engineering, computer science, and advanced mathematics. These skills prepare you for calculus and computational problem-solving in real-world applications.

Before You Start — Make Sure You Can:

Solving linear equations using multiplication and divisionSolving two-step linear equations: ax + b = c, x/a + b = cSolving literal equationsPower rule

This Unit Includes

11 Video lessons
Practice exercises
Learning resources

Skills

Iteration
Direct Iteration
Bisection Method
Newton-Raphson
Polynomial Equations
Numerical Methods
Approximation
Derivatives
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