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

The solutions to the equation 3x^3+x-1=0 are x\approx 0.53656…

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

The zeros of 3x^3+x-1=0 are x\approx 0.53656…

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

x \approx 0.53656 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.53656 \dots

Apply long division:

\frac{3 x ^{3} + x - 1}{x - 0.53656 \dots} = 3 x^{2} + 1.60969 \dots x + 1.86370 \dots

3 x^{2} + 1.60969 \dots x + 1.86370 \dots \approx 0

Find one solution for

3 x^{2} + 1.60969 \dots x + 1.86370 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.53656 \dots

- 8 = p^{3}

x, f = 4 x^{3} + 2

5 x^{3} + 11 x^{2} + 7 x + 1 = 0

4 x^{3} - 24 x + 1 = 0

x (x - 1)^{2} = 1

What are the solutions to the equation 3x^3+x-1=0 ?
The solutions to the equation 3x^3+x-1=0 are x\approx 0.53656…
Find the zeros of 3x^3+x-1=0
The zeros of 3x^3+x-1=0 are x\approx 0.53656…