What are the solutions to the equation 8x^3-6x-1=0 ?

The solutions to the equation 8x^3-6x-1=0 are x\approx-0.17364…,x\approx-0.76604…,x\approx 0.93969…

Find the zeros of 8x^3-6x-1=0

The zeros of 8x^3-6x-1=0 are x\approx-0.17364…,x\approx-0.76604…,x\approx 0.93969…

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

x \approx - 0.17364 \dots, x \approx - 0.76604 \dots, x \approx 0.93969 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx - 0.17364 \dots

Apply long division:

\frac{8 x ^{3} - 6 x - 1}{x + 0.17364 \dots} = 8 x^{2} - 1.38918 \dots x - 5.75877 \dots

8 x^{2} - 1.38918 \dots x - 5.75877 \dots \approx 0

Find one solution for

8 x^{2} - 1.38918 \dots x - 5.75877 \dots = 0

using Newton-Raphson:

x \approx - 0.76604 \dots

Apply long division:

\frac{8 x ^{2} - 1.38918 \dots x - 5.75877 \dots}{x + 0.76604 \dots} = 8 x - 7.51754 \dots

8 x - 7.51754 \dots \approx 0

x \approx 0.93969 \dots

The solutions are

x \approx - 0.17364 \dots, x \approx - 0.76604 \dots, x \approx 0.93969 \dots

x^{4} = 64

3 a^{5} - a^{2} = 120

2 x^{3} = - 98 x

2 x^{3} - 16 x^{2} + 30 x = 0

3 x^{8} - 4 x^{3} = 4

What are the solutions to the equation 8x^3-6x-1=0 ?
The solutions to the equation 8x^3-6x-1=0 are x\approx-0.17364…,x\approx-0.76604…,x\approx 0.93969…
Find the zeros of 8x^3-6x-1=0
The zeros of 8x^3-6x-1=0 are x\approx-0.17364…,x\approx-0.76604…,x\approx 0.93969…