# 1) Find the multiplicity root of the equation x^3-x^2-x+1=0 near x0 = 0.9. And 2) Find the solution of the following system of equations. x-1/4y-1/4z=1/2 -1/4x+y-1/4w=1/2 -1/4x+z-1/4w=1/2...

1) Find the multiplicity root of the equation x^3-x^2-x+1=0 near x0 = 0.9.

And

2) Find the solution of the following system of equations.

x-1/4y-1/4z=1/2

-1/4x+y-1/4w=1/2

-1/4x+z-1/4w=1/2

-1/4y-1/4z+w=1/2

using Gauss-Seidel method and perform the first five iterations.

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Student Comments

aruv | Student

Define

`f(x)=x^3-x^2-x+1`

`f(1)=1-1-1+1=0`

This implies x=1 is one root of equation

`x^3-x^2-x+1=0`

Let factor the equation

`x^2(x-1)-1(x-1)=0`

`(x-1)(x^2-1)=0`

`(x-1)(x-1)(x+1)=0`

`(x-1)^2(x+1)=0`

Thus

multiplicity of root x=1 is 2.

multiplicity of root x=-1 is -1

Please repost second question enotes rule does not permit me to answer multi question.