What are the solutions to the equation x^4-6x^3+x^2-6x+1=0 ?

The solutions to the equation x^4-6x^3+x^2-6x+1=0 are x\approx 0.16679…,x\approx 5.99548…

Find the zeros of x^4-6x^3+x^2-6x+1=0

The zeros of x^4-6x^3+x^2-6x+1=0 are x\approx 0.16679…,x\approx 5.99548…

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x^{4} - 6 x^{3} + x^{2} - 6 x + 1 = 0

x \approx 0.16679 \dots, x \approx 5.99548 \dots

Solution steps

x^{4} - 6 x^{3} + x^{2} - 6 x + 1 = 0

Find one solution for

x^{4} - 6 x^{3} + x^{2} - 6 x + 1 = 0

using Newton-Raphson:

x \approx 0.16679 \dots

Apply long division:

\frac{x ^{4} - 6 x ^{3} + x ^{2} - 6 x + 1}{x - 0.16679 \dots} = x^{3} - 5.83320 \dots x^{2} + 0.02706 \dots x - 5.99548 \dots

x^{3} - 5.83320 \dots x^{2} + 0.02706 \dots x - 5.99548 \dots \approx 0

Find one solution for

x^{3} - 5.83320 \dots x^{2} + 0.02706 \dots x - 5.99548 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

x \approx 5.99548 \dots

The solutions are

x \approx 0.16679 \dots, x \approx 5.99548 \dots

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

3 x^{3} = 9

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

3 x^{3} = 2

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

What are the solutions to the equation x^4-6x^3+x^2-6x+1=0 ?
The solutions to the equation x^4-6x^3+x^2-6x+1=0 are x\approx 0.16679…,x\approx 5.99548…
Find the zeros of x^4-6x^3+x^2-6x+1=0
The zeros of x^4-6x^3+x^2-6x+1=0 are x\approx 0.16679…,x\approx 5.99548…