What are the solutions to the equation r^3-3r^2+2r-1=0 ?

The solutions to the equation r^3-3r^2+2r-1=0 are r\approx 2.32471…

Find the zeros of r^3-3r^2+2r-1=0

The zeros of r^3-3r^2+2r-1=0 are r\approx 2.32471…

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r^{3} - 3 r^{2} + 2 r - 1 = 0

r \approx 2.32471 \dots

Solution steps

r^{3} - 3 r^{2} + 2 r - 1 = 0

Find one solution for

r^{3} - 3 r^{2} + 2 r - 1 = 0

using Newton-Raphson:

r \approx 2.32471 \dots

Apply long division:

\frac{r ^{3} - 3 r ^{2} + 2 r - 1}{r - 2.32471 \dots} = r^{2} - 0.67528 \dots r + 0.43015 \dots

r^{2} - 0.67528 \dots r + 0.43015 \dots \approx 0

Find one solution for

r^{2} - 0.67528 \dots r + 0.43015 \dots = 0

using Newton-Raphson:

No Solution for

r \in R

The solution is

r \approx 2.32471 \dots

x^{2} (4 x + 5) - (4 x + 5) = 0

x^{3} - 11 x^{2} - 11 x + 121 = 0

x^{3} + 5 x^{2} - 36 x - 180 = 0

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

8 x^{4} + 27 = 0

What are the solutions to the equation r^3-3r^2+2r-1=0 ?
The solutions to the equation r^3-3r^2+2r-1=0 are r\approx 2.32471…
Find the zeros of r^3-3r^2+2r-1=0
The zeros of r^3-3r^2+2r-1=0 are r\approx 2.32471…