Solving polynomial equations by iteration
Intros
Lessons
Examples
Lessons
- Solving Equations Using Direct Iteration
- Solving Equations Using Direct Iteration
- Evaluating equations Using Iteration by Bisection
The equation x3+5x−7=91 has a solution between 4 and 5. Use bisection iteration to find the solution and give the answer to 1 decimal place. - Use bisection iteration to solve x3−x2=39. Give your answer to 1 decimal place.
- Analyzing Equations Using Newton-Raphson Method
Given x2−6x+5=0.
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Topic Notes
In this lesson, we will learn:
- Solving Equations Using Direct Iteration
- Evaluating equations Using Iteration by Bisection
- Analyzing Equations Using Newton-Raphson Method
• Direct iteration:
1. Rearrange the original equation such that the term in which the variable with the highest exponent is isolated.
2. Leave the variable on its own on the LHS by performing inverse operation.
3. The LHS becomes xn+1.
4. The RHS becomes xn.
• Iteration by bisection:
1. Shrink the interval where the roots lies within 2 equal parts.
2. Decide in which part the solution resides.
3. Repeat the steps until a consistent answer is achieved.
• Newton-Raphson method:
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