What are the solutions to the equation x^4-6x^3+20x^2-22x-13=0 ?

The solutions to the equation x^4-6x^3+20x^2-22x-13=0 are x=-sqrt(2)+1,x=sqrt(2)+1

Find the zeros of x^4-6x^3+20x^2-22x-13=0

The zeros of x^4-6x^3+20x^2-22x-13=0 are x=-sqrt(2)+1,x=sqrt(2)+1

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x^{4} - 6 x^{3} + 20 x^{2} - 22 x - 13 = 0

x = - 2 + 1, x = 2 + 1

Decimal Notation

x = - 0.41421 \dots, x = 2.41421 \dots

Solution steps

x^{4} - 6 x^{3} + 20 x^{2} - 22 x - 13 = 0

Find one solution for

x^{4} - 6 x^{3} + 20 x^{2} - 22 x - 13 = 0

using Newton-Raphson:

x \approx - 0.41421 \dots

Apply long division:

\frac{x ^{4} - 6 x ^{3} + 20 x ^{2} - 22 x - 13}{x + 0.41421 \dots} = x^{3} - 6.41421 \dots x^{2} + 22.65685 \dots x - 31.38477 \dots

x^{3} - 6.41421 \dots x^{2} + 22.65685 \dots x - 31.38477 \dots \approx 0

Find one solution for

x^{3} - 6.41421 \dots x^{2} + 22.65685 \dots x - 31.38477 \dots = 0

using Newton-Raphson:

x \approx 2.41421 \dots

Apply long division:

\frac{x ^{3} - 6.41421 \dots x ^{2} + 22.65685 \dots x - 31.38477 \dots}{x - 2.41421 \dots} = x^{2} - 4 x + 13

x^{2} - 4 x + 13 \approx 0

Find one solution for

x^{2} - 4 x + 13 = 0

using Newton-Raphson:

No Solution for

x \in R

Approximate to algebraic form

x \approx - 0.41421 \dots : x = - 2 + 1

x \approx 2.41421 \dots : x = 2 + 1

x = - 2 + 1, x = 2 + 1

The solutions are

x = - 2 + 1, x = 2 + 1

(x - 1) (x^{2} - 13) = 0

x^{3} + 6 x^{2} - 11 x + 6 = 0

1 x^{3} - 4 x^{2} + 1 x + 6 = 0

x^{3} - 2 x^{2} - 15 x + 30 = 0

x^{5} - x^{3} + 3 x - 5 = 0

What are the solutions to the equation x^4-6x^3+20x^2-22x-13=0 ?
The solutions to the equation x^4-6x^3+20x^2-22x-13=0 are x=-sqrt(2)+1,x=sqrt(2)+1
Find the zeros of x^4-6x^3+20x^2-22x-13=0
The zeros of x^4-6x^3+20x^2-22x-13=0 are x=-sqrt(2)+1,x=sqrt(2)+1