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

The solutions to the equation 3x^3-3x+1=0 are x\approx 0.39493…,x\approx 0.74222…,x\approx-1.13715…

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

The zeros of 3x^3-3x+1=0 are x\approx 0.39493…,x\approx 0.74222…,x\approx-1.13715…

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

x \approx 0.39493 \dots, x \approx 0.74222 \dots, x \approx - 1.13715 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.39493 \dots

Apply long division:

\frac{3 x ^{3} - 3 x + 1}{x - 0.39493 \dots} = 3 x^{2} + 1.18479 \dots x - 2.53208 \dots

3 x^{2} + 1.18479 \dots x - 2.53208 \dots \approx 0

Find one solution for

3 x^{2} + 1.18479 \dots x - 2.53208 \dots = 0

using Newton-Raphson:

x \approx 0.74222 \dots

Apply long division:

\frac{3 x ^{2} + 1.18479 \dots x - 2.53208 \dots}{x - 0.74222 \dots} = 3 x + 3.41147 \dots

3 x + 3.41147 \dots \approx 0

x \approx - 1.13715 \dots

The solutions are

x \approx 0.39493 \dots, x \approx 0.74222 \dots, x \approx - 1.13715 \dots

x^{4} + 3 x^{2} - 28 = 0

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

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

512 x^{3} = 8

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

What are the solutions to the equation 3x^3-3x+1=0 ?
The solutions to the equation 3x^3-3x+1=0 are x\approx 0.39493…,x\approx 0.74222…,x\approx-1.13715…
Find the zeros of 3x^3-3x+1=0
The zeros of 3x^3-3x+1=0 are x\approx 0.39493…,x\approx 0.74222…,x\approx-1.13715…