What are the solutions to the equation x^3-6x+1=0 ?

The solutions to the equation x^3-6x+1=0 are x\approx 0.16744…,x\approx 2.36146…,x\approx-2.52891…

Find the zeros of x^3-6x+1=0

The zeros of x^3-6x+1=0 are x\approx 0.16744…,x\approx 2.36146…,x\approx-2.52891…

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

x \approx 0.16744 \dots, x \approx 2.36146 \dots, x \approx - 2.52891 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.16744 \dots

Apply long division:

\frac{x ^{3} - 6 x + 1}{x - 0.16744 \dots} = x^{2} + 0.16744 \dots x - 5.97196 \dots

x^{2} + 0.16744 \dots x - 5.97196 \dots \approx 0

Find one solution for

x^{2} + 0.16744 \dots x - 5.97196 \dots = 0

using Newton-Raphson:

x \approx 2.36146 \dots

Apply long division:

\frac{x ^{2} + 0.16744 \dots x - 5.97196 \dots}{x - 2.36146 \dots} = x + 2.52891 \dots

x + 2.52891 \dots \approx 0

x \approx - 2.52891 \dots

The solutions are

x \approx 0.16744 \dots, x \approx 2.36146 \dots, x \approx - 2.52891 \dots

x^{3} - 25 x = 0

y, x = y^{4}

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

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

5 x^{3} + 30 x^{2} + 45 x = 0

What are the solutions to the equation x^3-6x+1=0 ?
The solutions to the equation x^3-6x+1=0 are x\approx 0.16744…,x\approx 2.36146…,x\approx-2.52891…
Find the zeros of x^3-6x+1=0
The zeros of x^3-6x+1=0 are x\approx 0.16744…,x\approx 2.36146…,x\approx-2.52891…