What are the solutions to the equation x^3-6x+2=0 ?

The solutions to the equation x^3-6x+2=0 are x\approx 0.33987…,x\approx 2.26180…,x\approx-2.60167…

Find the zeros of x^3-6x+2=0

The zeros of x^3-6x+2=0 are x\approx 0.33987…,x\approx 2.26180…,x\approx-2.60167…

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

x \approx 0.33987 \dots, x \approx 2.26180 \dots, x \approx - 2.60167 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.33987 \dots

Apply long division:

\frac{x ^{3} - 6 x + 2}{x - 0.33987 \dots} = x^{2} + 0.33987 \dots x - 5.88448 \dots

x^{2} + 0.33987 \dots x - 5.88448 \dots \approx 0

Find one solution for

x^{2} + 0.33987 \dots x - 5.88448 \dots = 0

using Newton-Raphson:

x \approx 2.26180 \dots

Apply long division:

\frac{x ^{2} + 0.33987 \dots x - 5.88448 \dots}{x - 2.26180 \dots} = x + 2.60167 \dots

x + 2.60167 \dots \approx 0

x \approx - 2.60167 \dots

The solutions are

x \approx 0.33987 \dots, x \approx 2.26180 \dots, x \approx - 2.60167 \dots

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

x^{3} + 4 x^{2} - 10 = 0

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

x^{3} - 6 x^{2} + 9 x = 0

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

What are the solutions to the equation x^3-6x+2=0 ?
The solutions to the equation x^3-6x+2=0 are x\approx 0.33987…,x\approx 2.26180…,x\approx-2.60167…
Find the zeros of x^3-6x+2=0
The zeros of x^3-6x+2=0 are x\approx 0.33987…,x\approx 2.26180…,x\approx-2.60167…