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

Decimal Notation

x = 0.26794 \dots, x = 3.73205 \dots

Solution steps

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

x^{3} - 2 x^{2} + 25 x - 50 = 0

x^{3} + x^{2} = 9 x + 9

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

x^{4} - 4 x^{3} + 8 x^{2} - 16 x + 16 = 0

w^{3} = 512

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