What are the solutions to the equation x^4-8x+1=0 ?

The solutions to the equation x^4-8x+1=0 are x\approx 0.12503…,x\approx 1.95646…

Find the zeros of x^4-8x+1=0

The zeros of x^4-8x+1=0 are x\approx 0.12503…,x\approx 1.95646…

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x^{4} - 8 x + 1 = 0

x \approx 0.12503 \dots, x \approx 1.95646 \dots

Solution steps

x^{4} - 8 x + 1 = 0

Find one solution for

x^{4} - 8 x + 1 = 0

using Newton-Raphson:

x \approx 0.12503 \dots

Apply long division:

\frac{x ^{4} - 8 x + 1}{x - 0.12503 \dots} = x^{3} + 0.12503 \dots x^{2} + 0.01563 \dots x - 7.99804 \dots

x^{3} + 0.12503 \dots x^{2} + 0.01563 \dots x - 7.99804 \dots \approx 0

Find one solution for

x^{3} + 0.12503 \dots x^{2} + 0.01563 \dots x - 7.99804 \dots = 0

using Newton-Raphson:

x \approx 1.95646 \dots

Apply long division:

\frac{x ^{3} + 0.12503 \dots x ^{2} + 0.01563 \dots x - 7.99804 \dots}{x - 1.95646 \dots} = x^{2} + 2.08149 \dots x + 4.08800 \dots

x^{2} + 2.08149 \dots x + 4.08800 \dots \approx 0

Find one solution for

x^{2} + 2.08149 \dots x + 4.08800 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.12503 \dots, x \approx 1.95646 \dots

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

2 x + 4 = x^{3}

x^{4} - 10 x^{2} + 9

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

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

What are the solutions to the equation x^4-8x+1=0 ?
The solutions to the equation x^4-8x+1=0 are x\approx 0.12503…,x\approx 1.95646…
Find the zeros of x^4-8x+1=0
The zeros of x^4-8x+1=0 are x\approx 0.12503…,x\approx 1.95646…