Question

using your calculator or graphing calculator, find an approximation of all the roots of the equation below to nine decimal places using Newton's method. list the iterations leading to the solutions.

F(x)=X^{3}-3x^{2}+6x+2

Answer #1

For any initial value this method gives only -0. 287909751 solution.

It means that other two solutions are complex number

A graphing calculator is recommended.
Use Newton's method to find all solutions of the equation
correct to eight decimal places. Start by drawing a graph to find
initial approximations. (Enter your answers as a comma-separated
list.)
−3x7 − 5x4 + 9x3 + 7 = 0
x =

Use Newton's method with the specified initial approximation
x1 to find x3, the third
approximation to the root of the given equation.
x3 + 5x − 2 =
0, x1 = 2
Step 1
If
f(x) =
x3 + 5x − 2,
then
f'(x) = _____ x^2 + _____
2- Use Newton's method to find all roots of the
equation correct to six decimal places. (Enter your answers as a
comma-separated list.)
x4 = 5 + x
.

A graphing calculator is recommended.
Use Newton's method to find all solutions of the equation correct
to eight decimal places. Start by drawing a graph to find initial
approximations. (Enter your answers as a comma-separated list.)
−2x7 − 5x4 + 9x3 + 2 = 0

A graphing calculator is recommended. Use Newton's method to
find all solutions of the equation correct to eight decimal places.
Start by drawing a graph to find initial approximations. (Enter
your answers as a comma-separated list.) -2x^7-4x^4+9x^3+2=0

3.8/3.9
5. Use Newton's Method to approximate the zero(s) of the
function. Continue the iterations until two successive
approximations differ by less than 0.001. Then find the zero(s) to
three decimal places using a graphing utility and compare the
results.
f(x) = 3 − x + sin(x)
Newton's Method: x=
Graphing Utility: x=
6. Find the tangent line approximation T to the graph
of f at the given point. Then complete the table. (Round
your answer to four decimal places.)...

8. (a) Use Newton's method to find all solutions of the equation
correct to six decimal places. (Enter your answers as a
comma-separated list.) sqrt(x + 4) = x^2 − x 2.
(b) Use Newton's method to find the critical numbers of the
function: f(x) = x^6 − x^4 + 4x^3 − 3x, correct to six decimal
places. (Enter your answers as a comma-separated list.) x =

Find all the roots of the cubic polynomial x3 − 3x2 − 6x − 20
using Cardan’s formula. (Note: This polynomial is easily factored.
Use this to check your answer.) can you explain this step by step
and clearly explain what you are doing!

Find all solutions of the equation. (Enter all answers including
repetitions. Enter your answers as a comma-separated list.)
x4 + 5x3− 17x2− 15x
+ 42 = 0
Find all solutions of the equation. (Enter
all
answers including repetitions. Enter your
answers as a comma-separated list.)
6x5 + 43x4 + 37x3 − 30x2 = 0
Find all solutions of the equation. (Enter
all answers including repetitions. Enter your answers as a
comma-separated list.)
x3 − 8x2 − 19x − 10...

Use Newton's method with the specified initial approximation x1
to find x3, the third approximation to the root of the given
equation. (Round your answer to four decimal places.) 2x^3 − 3x^2 +
2 = 0, x1 = −1

use
newtons method to find all roots of the equation correct to six
decimal places. Enter your answer as a comma separated list.
7cos x = 7 sqrt x

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