How can Vieta's methods be applied to determine all the roots of the polynomial f(x)=x^3−3x^2−1after the Newton-Raphson method has already obtained the root x=3.1038 with a precision of 10−4? To Find: Roots of polynomial to a precision of 10-4Given f(x) = x²³-3x²-1. ε = 10-4EUsing Newton-Raphson method,f(x)Formula used:Хан Хи-11хаf (xn)1st iteration: n =ox₁ = x₁= f (xo)f'(xo)f'(x)= x3-3rd iteration: n=2x3 = x₂- f (x₂)f'(x₂)f(3)= -1 <0f (4) = 15>0Root lies between 3 and 43+43,5xo2nd iteration: n=1x₂ = x₁ - f (x₁) = 3.1146-f'(x₁): 3.5- f (3.5) 3.5- 5.12515.75f (3.5)4th iteration; n = 3;f (x3)f'(x3)f(x) = x³ 3x²-1f'(x) = _d (x²³²-3x²-1) = 3x²³²-6xdx= 3.10669-f(3.1746)f(3-1746)3= 3-10381 -= 3.10669f(3.10669)f'(3.10669)f(3.10381)f'(3.10381)= 3.1746= 3.10381= 3.1038114-31 = 13.1038-3.10381 | ≤ 10 = E+Root obtained with accuracy & = 10 + after 4iterations, x ~3.1038.:: Root of polynomial, ~3.1038.

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Answered: How can Vieta's methods be applied to…

How can Vieta's methods be applied to determine all the roots of the polynomial f(x)=x^3−3x^2−1after the Newton-Raphson method has already obtained the root x=3.1038 with a precision of 10−4?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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