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

The solutions to the equation x^3-9x+1=0 are x\approx 0.11126…,x\approx 2.94282…,x\approx-3.05408…

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

The zeros of x^3-9x+1=0 are x\approx 0.11126…,x\approx 2.94282…,x\approx-3.05408…

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

x \approx 0.11126 \dots, x \approx 2.94282 \dots, x \approx - 3.05408 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.11126 \dots

Apply long division:

\frac{x ^{3} - 9 x + 1}{x - 0.11126 \dots} = x^{2} + 0.11126 \dots x - 8.98762 \dots

x^{2} + 0.11126 \dots x - 8.98762 \dots \approx 0

Find one solution for

x^{2} + 0.11126 \dots x - 8.98762 \dots = 0

using Newton-Raphson:

x \approx 2.94282 \dots

Apply long division:

\frac{x ^{2} + 0.11126 \dots x - 8.98762 \dots}{x - 2.94282 \dots} = x + 3.05408 \dots

x + 3.05408 \dots \approx 0

x \approx - 3.05408 \dots

The solutions are

x \approx 0.11126 \dots, x \approx 2.94282 \dots, x \approx - 3.05408 \dots

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

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

16 x^{2} - 60 x - x^{3} = 0

x^{4} - 53 x^{2} + 196 = 0

y^{6} + y = 0

What are the solutions to the equation x^3-9x+1=0 ?
The solutions to the equation x^3-9x+1=0 are x\approx 0.11126…,x\approx 2.94282…,x\approx-3.05408…
Find the zeros of x^3-9x+1=0
The zeros of x^3-9x+1=0 are x\approx 0.11126…,x\approx 2.94282…,x\approx-3.05408…