What are the solutions to the equation x^3-5x+1=0 ?

The solutions to the equation x^3-5x+1=0 are x\approx 0.20163…,x\approx 2.12841…,x\approx-2.33005…

Find the zeros of x^3-5x+1=0

The zeros of x^3-5x+1=0 are x\approx 0.20163…,x\approx 2.12841…,x\approx-2.33005…

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x^{3} - 5 x + 1 = 0

x \approx 0.20163 \dots, x \approx 2.12841 \dots, x \approx - 2.33005 \dots

Solution steps

x^{3} - 5 x + 1 = 0

Find one solution for

x^{3} - 5 x + 1 = 0

using Newton-Raphson:

x \approx 0.20163 \dots

Apply long division:

\frac{x ^{3} - 5 x + 1}{x - 0.20163 \dots} = x^{2} + 0.20163 \dots x - 4.95934 \dots

x^{2} + 0.20163 \dots x - 4.95934 \dots \approx 0

Find one solution for

x^{2} + 0.20163 \dots x - 4.95934 \dots = 0

using Newton-Raphson:

x \approx 2.12841 \dots

Apply long division:

\frac{x ^{2} + 0.20163 \dots x - 4.95934 \dots}{x - 2.12841 \dots} = x + 2.33005 \dots

x + 2.33005 \dots \approx 0

x \approx - 2.33005 \dots

The solutions are

x \approx 0.20163 \dots, x \approx 2.12841 \dots, x \approx - 2.33005 \dots

x^{5} - 32 i = 0

4 x^{5} = - 4 x^{3}

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

x^{3} + 2 x^{2} - 25 x - 50 = 0

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

What are the solutions to the equation x^3-5x+1=0 ?
The solutions to the equation x^3-5x+1=0 are x\approx 0.20163…,x\approx 2.12841…,x\approx-2.33005…
Find the zeros of x^3-5x+1=0
The zeros of x^3-5x+1=0 are x\approx 0.20163…,x\approx 2.12841…,x\approx-2.33005…