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

The solutions to the equation x^4-2x^3+4x-1=0 are x\approx 0.25743…,x\approx-1.22269…

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

The zeros of x^4-2x^3+4x-1=0 are x\approx 0.25743…,x\approx-1.22269…

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

x \approx 0.25743 \dots, x \approx - 1.22269 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.25743 \dots

Apply long division:

\frac{x ^{4} - 2 x ^{3} + 4 x - 1}{x - 0.25743 \dots} = x^{3} - 1.74256 \dots x^{2} - 0.44859 \dots x + 3.88451 \dots

x^{3} - 1.74256 \dots x^{2} - 0.44859 \dots x + 3.88451 \dots \approx 0

Find one solution for

x^{3} - 1.74256 \dots x^{2} - 0.44859 \dots x + 3.88451 \dots = 0

using Newton-Raphson:

x \approx - 1.22269 \dots

Apply long division:

\frac{x ^{3} - 1.74256 \dots x ^{2} - 0.44859 \dots x + 3.88451 \dots}{x + 1.22269 \dots} = x^{2} - 2.96526 \dots x + 3.17701 \dots

x^{2} - 2.96526 \dots x + 3.17701 \dots \approx 0

Find one solution for

x^{2} - 2.96526 \dots x + 3.17701 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.25743 \dots, x \approx - 1.22269 \dots

x, (x) 8 x^{2} + 4 y^{2} = 12

x^{5} - 2 x = 0

x^{5} = 1460

x, x^{4} - 10 x^{2} + 9 = 0

x^{4} + 4 x^{3} - 2 x^{2} + 9 = 0

What are the solutions to the equation x^4-2x^3+4x-1=0 ?
The solutions to the equation x^4-2x^3+4x-1=0 are x\approx 0.25743…,x\approx-1.22269…
Find the zeros of x^4-2x^3+4x-1=0
The zeros of x^4-2x^3+4x-1=0 are x\approx 0.25743…,x\approx-1.22269…