What are the solutions to the equation (x^3)/3-x^2+x+1=0 ?

The solutions to the equation (x^3)/3-x^2+x+1=0 are x\approx-0.58740…

Find the zeros of (x^3)/3-x^2+x+1=0

The zeros of (x^3)/3-x^2+x+1=0 are x\approx-0.58740…

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\frac{x ^{3}}{3} - x^{2} + x + 1 = 0

x \approx - 0.58740 \dots

Solution steps

\frac{x ^{3}}{3} - x^{2} + x + 1 = 0

Multiply both sides by

3

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

Find one solution for

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

using Newton-Raphson:

x \approx - 0.58740 \dots

Apply long division:

\frac{x ^{3} - 3 x ^{2} + 3 x + 3}{x + 0.58740 \dots} = x^{2} - 3.58740 \dots x + 5.10724 \dots

x^{2} - 3.58740 \dots x + 5.10724 \dots \approx 0

Find one solution for

x^{2} - 3.58740 \dots x + 5.10724 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 0.58740 \dots

x, 0 = x^{4} - 8 x^{2} - 9

43 = a^{3}

x^{8} + 4 x^{2} + 4 = 0

- y^{3} + y^{2} - 5 y = 24

z^{4} - z^{3} + z^{2} - z + 1 = 0

What are the solutions to the equation (x^3)/3-x^2+x+1=0 ?
The solutions to the equation (x^3)/3-x^2+x+1=0 are x\approx-0.58740…
Find the zeros of (x^3)/3-x^2+x+1=0
The zeros of (x^3)/3-x^2+x+1=0 are x\approx-0.58740…