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

The solutions to the equation x^3-9x+3=0 are x\approx 0.33760…,x\approx 2.81691…,x\approx-3.15452…

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

The zeros of x^3-9x+3=0 are x\approx 0.33760…,x\approx 2.81691…,x\approx-3.15452…

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

x \approx 0.33760 \dots, x \approx 2.81691 \dots, x \approx - 3.15452 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.33760 \dots

Apply long division:

\frac{x ^{3} - 9 x + 3}{x - 0.33760 \dots} = x^{2} + 0.33760 \dots x - 8.88602 \dots

x^{2} + 0.33760 \dots x - 8.88602 \dots \approx 0

Find one solution for

x^{2} + 0.33760 \dots x - 8.88602 \dots = 0

using Newton-Raphson:

x \approx 2.81691 \dots

Apply long division:

\frac{x ^{2} + 0.33760 \dots x - 8.88602 \dots}{x - 2.81691 \dots} = x + 3.15452 \dots

x + 3.15452 \dots \approx 0

x \approx - 3.15452 \dots

The solutions are

x \approx 0.33760 \dots, x \approx 2.81691 \dots, x \approx - 3.15452 \dots

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

7 x^{2} (3 x - 5) = 0

48 x^{5} = 27 x^{3}

x^{8} + 4 x^{6} - 4 x^{2} - 1 = 0

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

What are the solutions to the equation x^3-9x+3=0 ?
The solutions to the equation x^3-9x+3=0 are x\approx 0.33760…,x\approx 2.81691…,x\approx-3.15452…
Find the zeros of x^3-9x+3=0
The zeros of x^3-9x+3=0 are x\approx 0.33760…,x\approx 2.81691…,x\approx-3.15452…