The values of various roots can be approximated using Newton's method. For example, to approximate the value of 10, let x = V10 and cube both sides of the equation to obtain x = 10, or x' - 10 = 0. Therefore, V10 is a root of p(x) =x° - 10, which can be approximated by applying Newton's method. Approximate the following value of r by first finding a polynomial with integer coefficients that has a root r. Use an appropriate value of x, and stop calculating approximations when two successive approximations agree to five digits to th right of the decimal point after rounding. 1 r= 11 (Type an integer or decimal rounded to five decimal places as needed.)

The values of various roots can be approximated using Newton's method. For example, to approximate the value of 10, let x = V10 and cube both sides of the equation to obtain x = 10, or x' - 10 = 0. Therefore, V10 is a root of p(x) =x° - 10, which can be approximated by applying Newton's method. Approximate the following value of r by first finding a polynomial with integer coefficients that has a root r. Use an appropriate value of x, and stop calculating approximations when two successive approximations agree to five digits to th right of the decimal point after rounding. 1 r= 11 (Type an integer or decimal rounded to five decimal places as needed.)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 66E

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