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

The solutions to the equation x^4-2x^3+3x-1=0 are x\approx 0.35855…,x\approx-1.11768…

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

The zeros of x^4-2x^3+3x-1=0 are x\approx 0.35855…,x\approx-1.11768…

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

x \approx 0.35855 \dots, x \approx - 1.11768 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.35855 \dots

Apply long division:

\frac{x ^{4} - 2 x ^{3} + 3 x - 1}{x - 0.35855 \dots} = x^{3} - 1.64144 \dots x^{2} - 0.58854 \dots x + 2.78897 \dots

x^{3} - 1.64144 \dots x^{2} - 0.58854 \dots x + 2.78897 \dots \approx 0

Find one solution for

x^{3} - 1.64144 \dots x^{2} - 0.58854 \dots x + 2.78897 \dots = 0

using Newton-Raphson:

x \approx - 1.11768 \dots

Apply long division:

\frac{x ^{3} - 1.64144 \dots x ^{2} - 0.58854 \dots x + 2.78897 \dots}{x + 1.11768 \dots} = x^{2} - 2.75913 \dots x + 2.49530 \dots

x^{2} - 2.75913 \dots x + 2.49530 \dots \approx 0

Find one solution for

x^{2} - 2.75913 \dots x + 2.49530 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.35855 \dots, x \approx - 1.11768 \dots

x^{11} = 2

λ^{3} - 6 λ^{2} + 11 λ - 6 = 0

x^{3} - 5 x - 10 = 0

x^{4} - 10 x^{2} + 1 = 0

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

What are the solutions to the equation x^4-2x^3+3x-1=0 ?
The solutions to the equation x^4-2x^3+3x-1=0 are x\approx 0.35855…,x\approx-1.11768…
Find the zeros of x^4-2x^3+3x-1=0
The zeros of x^4-2x^3+3x-1=0 are x\approx 0.35855…,x\approx-1.11768…