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

The solutions to the equation x^4+x^3-3x^2+3x-1=0 are x\approx 0.54970…,x\approx-2.62965…

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

The zeros of x^4+x^3-3x^2+3x-1=0 are x\approx 0.54970…,x\approx-2.62965…

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

x \approx 0.54970 \dots, x \approx - 2.62965 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.54970 \dots

Apply long division:

\frac{x ^{4} + x ^{3} - 3 x ^{2} + 3 x - 1}{x - 0.54970 \dots} = x^{3} + 1.54970 \dots x^{2} - 2.14812 \dots x + 1.81917 \dots

x^{3} + 1.54970 \dots x^{2} - 2.14812 \dots x + 1.81917 \dots \approx 0

Find one solution for

x^{3} + 1.54970 \dots x^{2} - 2.14812 \dots x + 1.81917 \dots = 0

using Newton-Raphson:

x \approx - 2.62965 \dots

Apply long division:

\frac{x ^{3} + 1.54970 \dots x ^{2} - 2.14812 \dots x + 1.81917 \dots}{x + 2.62965 \dots} = x^{2} - 1.07995 \dots x + 0.69179 \dots

x^{2} - 1.07995 \dots x + 0.69179 \dots \approx 0

Find one solution for

x^{2} - 1.07995 \dots x + 0.69179 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.54970 \dots, x \approx - 2.62965 \dots

w^{3} - 2 w^{2} + 2 - 2 = 0.2

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

x^{3} - 7 = 20

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

21494 = 35000 (1 + r)^{3}

What are the solutions to the equation x^4+x^3-3x^2+3x-1=0 ?
The solutions to the equation x^4+x^3-3x^2+3x-1=0 are x\approx 0.54970…,x\approx-2.62965…
Find the zeros of x^4+x^3-3x^2+3x-1=0
The zeros of x^4+x^3-3x^2+3x-1=0 are x\approx 0.54970…,x\approx-2.62965…