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

The solutions to the equation 0=x^3+x+1 are x\approx-0.68232…

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

The zeros of 0=x^3+x+1 are x\approx-0.68232…

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0 = x^{3} + x + 1

x \approx - 0.68232 \dots

Solution steps

0 = x^{3} + x + 1

Switch sides

x^{3} + x + 1 = 0

Find one solution for

x^{3} + x + 1 = 0

using Newton-Raphson:

x \approx - 0.68232 \dots

Apply long division:

\frac{x ^{3} + x + 1}{x + 0.68232 \dots} = x^{2} - 0.68232 \dots x + 1.46557 \dots

x^{2} - 0.68232 \dots x + 1.46557 \dots \approx 0

Find one solution for

x^{2} - 0.68232 \dots x + 1.46557 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 0.68232 \dots

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

4 x^{3} + 3 = 0

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

(12 - 3 x) \cdot (2 x - 1) x = 0

x^{3} - 0.75 x - 0.25 = 0

What are the solutions to the equation 0=x^3+x+1 ?
The solutions to the equation 0=x^3+x+1 are x\approx-0.68232…
Find the zeros of 0=x^3+x+1
The zeros of 0=x^3+x+1 are x\approx-0.68232…