What are the solutions to the equation 9x^3+3x^2-x-1=0 ?

The solutions to the equation 9x^3+3x^2-x-1=0 are x\approx 0.45310…

Find the zeros of 9x^3+3x^2-x-1=0

The zeros of 9x^3+3x^2-x-1=0 are x\approx 0.45310…

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9 x^{3} + 3 x^{2} - x - 1 = 0

x \approx 0.45310 \dots

Solution steps

9 x^{3} + 3 x^{2} - x - 1 = 0

Find one solution for

9 x^{3} + 3 x^{2} - x - 1 = 0

using Newton-Raphson:

x \approx 0.45310 \dots

Apply long division:

\frac{9 x ^{3} + 3 x ^{2} - x - 1}{x - 0.45310 \dots} = 9 x^{2} + 7.07791 \dots x + 2.20701 \dots

9 x^{2} + 7.07791 \dots x + 2.20701 \dots \approx 0

Find one solution for

9 x^{2} + 7.07791 \dots x + 2.20701 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.45310 \dots

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

9 y^{3} - 6 = y - 54 y^{2}

x^{20} = 2

x^{3} + x + 4 = 0

1 + y^{3} = 0

What are the solutions to the equation 9x^3+3x^2-x-1=0 ?
The solutions to the equation 9x^3+3x^2-x-1=0 are x\approx 0.45310…
Find the zeros of 9x^3+3x^2-x-1=0
The zeros of 9x^3+3x^2-x-1=0 are x\approx 0.45310…