Use Newton's Method to find the largest positive solution of x⁴ + 2x³ -2x² - 8x -10 = 0. A) 2.0542631 B) 2.0480128 C) 2.1395698 D) 2.4474034 E) 3.0548780

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Quizplus · Accepted Answer

Using Newton's Method, we start with an initial guess of $x=2$ and iterate using the formula $x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$ until we reach a desired level of accuracy. The derivative of the function is quite long, so we will not write it out here. After several iterations, we find that the largest positive solution to the equation is approximately $x=2.0480128$. This matches choice B.

Use Newton's Method to Find the Largest Positive Solution of X4

Use Newton's Method to Find the Largest Positive Solution of X⁴