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

The solutions to the equation 0=x^3-3x^2+3 are x\approx-0.87938…,x\approx 1.34729…,x\approx 2.53208…

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

The zeros of 0=x^3-3x^2+3 are x\approx-0.87938…,x\approx 1.34729…,x\approx 2.53208…

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

x \approx - 0.87938 \dots, x \approx 1.34729 \dots, x \approx 2.53208 \dots

Solution steps

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

Switch sides

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

Find one solution for

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

using Newton-Raphson:

x \approx - 0.87938 \dots

Apply long division:

\frac{x ^{3} - 3 x ^{2} + 3}{x + 0.87938 \dots} = x^{2} - 3.87938 \dots x + 3.41147 \dots

x^{2} - 3.87938 \dots x + 3.41147 \dots \approx 0

Find one solution for

x^{2} - 3.87938 \dots x + 3.41147 \dots = 0

using Newton-Raphson:

x \approx 1.34729 \dots

Apply long division:

\frac{x ^{2} - 3.87938 \dots x + 3.41147 \dots}{x - 1.34729 \dots} = x - 2.53208 \dots

x - 2.53208 \dots \approx 0

x \approx 2.53208 \dots

The solutions are

x \approx - 0.87938 \dots, x \approx 1.34729 \dots, x \approx 2.53208 \dots

4 x^{4} = 24 x^{2} + 108

z^{3} - 0.9887 z^{2} + 0.08362 z - 0.001075 = 0

y, x^{2} 2 x y + y^{2} = 1

12 x^{3} - 9 x^{2} + 4 x = 3

x^{4} - 6 x^{3} + 9 x^{2} + 4 x - 12 = 0

What are the solutions to the equation 0=x^3-3x^2+3 ?
The solutions to the equation 0=x^3-3x^2+3 are x\approx-0.87938…,x\approx 1.34729…,x\approx 2.53208…
Find the zeros of 0=x^3-3x^2+3
The zeros of 0=x^3-3x^2+3 are x\approx-0.87938…,x\approx 1.34729…,x\approx 2.53208…