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

The solutions to the equation x^5+x^3+x+1=0 are x\approx-0.63688…

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

The zeros of x^5+x^3+x+1=0 are x\approx-0.63688…

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x^{5} + x^{3} + x + 1 = 0

x \approx - 0.63688 \dots

Solution steps

x^{5} + x^{3} + x + 1 = 0

Find one solution for

x^{5} + x^{3} + x + 1 = 0

using Newton-Raphson:

x \approx - 0.63688 \dots

Apply long division:

\frac{x ^{5} + x ^{3} + x + 1}{x + 0.63688 \dots} = x^{4} - 0.63688 \dots x^{3} + 1.40561 \dots x^{2} - 0.89521 \dots x + 1.57014 \dots

x^{4} - 0.63688 \dots x^{3} + 1.40561 \dots x^{2} - 0.89521 \dots x + 1.57014 \dots \approx 0

Find one solution for

x^{4} - 0.63688 \dots x^{3} + 1.40561 \dots x^{2} - 0.89521 \dots x + 1.57014 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 0.63688 \dots

3 x^{4} - 4 x^{3} = 0

x^{5} - 7 x^{4} + 14 x^{3} - 2 x^{2} - 15 x + 9 = 0

x^{4} - 4 x^{3} - x^{2} + 14 x + 10

x^{4} + x^{2} + 1

X^{3} + 6 X^{2} = 4 X^{3} + 4 X^{2} - 5 X

What are the solutions to the equation x^5+x^3+x+1=0 ?
The solutions to the equation x^5+x^3+x+1=0 are x\approx-0.63688…
Find the zeros of x^5+x^3+x+1=0
The zeros of x^5+x^3+x+1=0 are x\approx-0.63688…