What are the solutions to the equation (x^4-3x^3-2x^2-3x+1)=0 ?

The solutions to the equation (x^4-3x^3-2x^2-3x+1)=0 are x=-sqrt(3)+2,x=sqrt(3)+2

Find the zeros of (x^4-3x^3-2x^2-3x+1)=0

The zeros of (x^4-3x^3-2x^2-3x+1)=0 are x=-sqrt(3)+2,x=sqrt(3)+2

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(x^{4} - 3 x^{3} - 2 x^{2} - 3 x + 1) = 0

x = - 3 + 2, x = 3 + 2

Solution steps

(x^{4} - 3 x^{3} - 2 x^{2} - 3 x + 1) = 0

Refine

x^{4} - 3 x^{3} - 2 x^{2} - 3 x + 1 = 0

Find one solution for

x^{4} - 3 x^{3} - 2 x^{2} - 3 x + 1 = 0

using Newton-Raphson:

x \approx 0.26794 \dots

Apply long division:

\frac{x ^{4} - 3 x ^{3} - 2 x ^{2} - 3 x + 1}{x - 0.26794 \dots} = x^{3} - 2.73205 \dots x^{2} - 2.73205 \dots x - 3.73205 \dots

x^{3} - 2.73205 \dots x^{2} - 2.73205 \dots x - 3.73205 \dots \approx 0

Find one solution for

x^{3} - 2.73205 \dots x^{2} - 2.73205 \dots x - 3.73205 \dots = 0

using Newton-Raphson:

x \approx 3.73205 \dots

Apply long division:

\frac{x ^{3} - 2.73205 \dots x ^{2} - 2.73205 \dots x - 3.73205 \dots}{x - 3.73205 \dots} = x^{2} + x + 1

x^{2} + x + 1 \approx 0

Find one solution for

x^{2} + x + 1 = 0

using Newton-Raphson:

No Solution for

x \in R

Approximate to algebraic form

x \approx 0.26794 \dots : x = - 3 + 2

x \approx 3.73205 \dots : x = 3 + 2

x = - 3 + 2, x = 3 + 2

The solutions are

x = - 3 + 2, x = 3 + 2

h^{3} = 64

\frac{( 35 x - 50 )}{5} = 2 x^{15}

- 10 x^{3} + 6 x^{2} + 90 x - 54 = 0

- y^{3} + 5 y^{2} - 7 y + 3 = 0

z^{3} = 1 + 3 i

What are the solutions to the equation (x^4-3x^3-2x^2-3x+1)=0 ?
The solutions to the equation (x^4-3x^3-2x^2-3x+1)=0 are x=-sqrt(3)+2,x=sqrt(3)+2
Find the zeros of (x^4-3x^3-2x^2-3x+1)=0
The zeros of (x^4-3x^3-2x^2-3x+1)=0 are x=-sqrt(3)+2,x=sqrt(3)+2