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

3 x^{4} + 2 = 5 x^{2}

x + 6 = x^{3}

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

27 x^{4} + 60 x^{2} = 32

3 (x - 1) (x + 2) (x - 4) = 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…