What are the solutions to the equation 3x^5-5x^4+2x^3-x^2+4x-1=0 ?

The solutions to the equation 3x^5-5x^4+2x^3-x^2+4x-1=0 are x\approx 0.26325…

Find the zeros of 3x^5-5x^4+2x^3-x^2+4x-1=0

The zeros of 3x^5-5x^4+2x^3-x^2+4x-1=0 are x\approx 0.26325…

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3 x^{5} - 5 x^{4} + 2 x^{3} - x^{2} + 4 x - 1 = 0

x \approx 0.26325 \dots

Solution steps

3 x^{5} - 5 x^{4} + 2 x^{3} - x^{2} + 4 x - 1 = 0

Find one solution for

3 x^{5} - 5 x^{4} + 2 x^{3} - x^{2} + 4 x - 1 = 0

using Newton-Raphson:

x \approx 0.26325 \dots

Apply long division:

\frac{3 x ^{5} - 5 x ^{4} + 2 x ^{3} - x ^{2} + 4 x - 1}{x - 0.26325 \dots} = 3 x^{4} - 4.21022 \dots x^{3} + 0.89161 \dots x^{2} - 0.76527 \dots x + 3.79853 \dots

3 x^{4} - 4.21022 \dots x^{3} + 0.89161 \dots x^{2} - 0.76527 \dots x + 3.79853 \dots \approx 0

Find one solution for

3 x^{4} - 4.21022 \dots x^{3} + 0.89161 \dots x^{2} - 0.76527 \dots x + 3.79853 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.26325 \dots

x^{4} - 2.3 x^{3} + 4 = 4

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

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

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

5 x^{3} = 405 x

What are the solutions to the equation 3x^5-5x^4+2x^3-x^2+4x-1=0 ?
The solutions to the equation 3x^5-5x^4+2x^3-x^2+4x-1=0 are x\approx 0.26325…
Find the zeros of 3x^5-5x^4+2x^3-x^2+4x-1=0
The zeros of 3x^5-5x^4+2x^3-x^2+4x-1=0 are x\approx 0.26325…