Use Newton's method to find the two real solutions of the equation: {eq}x^4 - x^3 - x^2 - 2x + 1 = 0 {/eq}.
Question:
Use Newton's method to find the two real solutions of the equation: {eq}x^4 - x^3 - x^2 - 2x + 1 = 0 {/eq}.
Finding Roots for a Fourth-Degree Polynomial with Newton's Method:
It is possible to find the real roots of a fourth degree polynomial with an iterative method such as Newton's method. To do this, it is necessary to construct a function from the polynomial, determine its first derivative and choose appropriately initial values for the iterative process.
Answer and Explanation: 1
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The equation is: {eq}\displaystyle x^4 - x^3 - x^2 - 2x + 1 \; = \; 0 {/eq}
The function is:
{eq}\displaystyle \ f(x) \, = \, x^4 - x^3 -...
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Chapter 10 / Lesson 4Understand what Newton's Method is. Learn about Newton's Method Formula and how to do Newton's Method. Get practical insights through various examples.