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

The solutions to the equation -x^3+3x+1=0 are x\approx-0.34729…,x\approx-1.53208…,x\approx 1.87938…

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

The zeros of -x^3+3x+1=0 are x\approx-0.34729…,x\approx-1.53208…,x\approx 1.87938…

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

x \approx - 0.34729 \dots, x \approx - 1.53208 \dots, x \approx 1.87938 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx - 0.34729 \dots

Apply long division:

\frac{- x ^{3} + 3 x + 1}{x + 0.34729 \dots} = - x^{2} + 0.34729 \dots x + 2.87938 \dots

- x^{2} + 0.34729 \dots x + 2.87938 \dots \approx 0

Find one solution for

- x^{2} + 0.34729 \dots x + 2.87938 \dots = 0

using Newton-Raphson:

x \approx - 1.53208 \dots

Apply long division:

\frac{- x ^{2} + 0.34729 \dots x + 2.87938 \dots}{x + 1.53208 \dots} = - x + 1.87938 \dots

- x + 1.87938 \dots \approx 0

x \approx 1.87938 \dots

The solutions are

x \approx - 0.34729 \dots, x \approx - 1.53208 \dots, x \approx 1.87938 \dots

x^{3} - 7 x^{2} + 4 x - 28 = 0

x^{4} - 21 x^{2} + 80 = 0

(\frac{4 x - 7}{3})^{3} = 27

x^{3} + 5 x^{2} = - 6 x

x, x^{3} - 2 x^{2} - 5 x + 6 = 0

What are the solutions to the equation -x^3+3x+1=0 ?
The solutions to the equation -x^3+3x+1=0 are x\approx-0.34729…,x\approx-1.53208…,x\approx 1.87938…
Find the zeros of -x^3+3x+1=0
The zeros of -x^3+3x+1=0 are x\approx-0.34729…,x\approx-1.53208…,x\approx 1.87938…