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

The solutions to the equation x^3-4x+1=0 are x\approx 0.25410…,x\approx 1.86080…,x\approx-2.11490…

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

The zeros of x^3-4x+1=0 are x\approx 0.25410…,x\approx 1.86080…,x\approx-2.11490…

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

x \approx 0.25410 \dots, x \approx 1.86080 \dots, x \approx - 2.11490 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.25410 \dots

Apply long division:

\frac{x ^{3} - 4 x + 1}{x - 0.25410 \dots} = x^{2} + 0.25410 \dots x - 3.93543 \dots

x^{2} + 0.25410 \dots x - 3.93543 \dots \approx 0

Find one solution for

x^{2} + 0.25410 \dots x - 3.93543 \dots = 0

using Newton-Raphson:

x \approx 1.86080 \dots

Apply long division:

\frac{x ^{2} + 0.25410 \dots x - 3.93543 \dots}{x - 1.86080 \dots} = x + 2.11490 \dots

x + 2.11490 \dots \approx 0

x \approx - 2.11490 \dots

The solutions are

x \approx 0.25410 \dots, x \approx 1.86080 \dots, x \approx - 2.11490 \dots

x^{1000} = 0.9

x^{3} - 3 x^{2} - 10 x + 24 = 0

(x^{2} + 1) (1 - 7 x) = 0

x^{4} - 4 x^{3} - 4 x^{2} - 10 = 0

x^{4} - 8 x^{2} + x + 12 = 0

What are the solutions to the equation x^3-4x+1=0 ?
The solutions to the equation x^3-4x+1=0 are x\approx 0.25410…,x\approx 1.86080…,x\approx-2.11490…
Find the zeros of x^3-4x+1=0
The zeros of x^3-4x+1=0 are x\approx 0.25410…,x\approx 1.86080…,x\approx-2.11490…