What are the solutions to the equation roots 1-x-x^3 ?

The solutions to the equation roots 1-x-x^3 are x\approx 0.68232…

Find the zeros of roots 1-x-x^3

The zeros of roots 1-x-x^3 are x\approx 0.68232…

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roots

1 - x - x^{3}

x \approx 0.68232 \dots

Solution steps

1 - x - x^{3}

The roots are the intercepts with the x-axis

(y = 0)

1 - x - x^{3} = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

- 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^{3} + (1 - x^{2})^{4} = 0

3 x^{3} + 4 x^{2} + 27 x + 36 = 0

d x^{3}

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

10 x + 0.5 x^{2} - 0.001 x^{3} - 5000 = 0

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