What are the solutions to the equation x^4-2x^3+2x^2-8x-8=0 ?

The solutions to the equation x^4-2x^3+2x^2-8x-8=0 are x\approx-0.73205…,x\approx 2.73205…

Find the zeros of x^4-2x^3+2x^2-8x-8=0

The zeros of x^4-2x^3+2x^2-8x-8=0 are x\approx-0.73205…,x\approx 2.73205…

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x^{4} - 2 x^{3} + 2 x^{2} - 8 x - 8 = 0

x \approx - 0.73205 \dots, x \approx 2.73205 \dots

Solution steps

x^{4} - 2 x^{3} + 2 x^{2} - 8 x - 8 = 0

Find one solution for

x^{4} - 2 x^{3} + 2 x^{2} - 8 x - 8 = 0

using Newton-Raphson:

x \approx - 0.73205 \dots

Apply long division:

\frac{x ^{4} - 2 x ^{3} + 2 x ^{2} - 8 x - 8}{x + 0.73205 \dots} = x^{3} - 2.73205 \dots x^{2} + 4.00000 \dots x - 10.92820 \dots

x^{3} - 2.73205 \dots x^{2} + 4.00000 \dots x - 10.92820 \dots \approx 0

Find one solution for

x^{3} - 2.73205 \dots x^{2} + 4.00000 \dots x - 10.92820 \dots = 0

using Newton-Raphson:

x \approx 2.73205 \dots

Apply long division:

\frac{x ^{3} - 2.73205 \dots x ^{2} + 4.00000 \dots x - 10.92820 \dots}{x - 2.73205 \dots} = x^{2} + 4

x^{2} + 4 \approx 0

Find one solution for

x^{2} + 4 = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 0.73205 \dots, x \approx 2.73205 \dots

x^{4} - 6 x^{2} - 8 x - 3 = 0

λ^{3} - 2 λ^{2} - 5 λ + 6 = 0

(4 b)^{4} = 2 b

64 j^{6} - 27 j^{3} = 0

3 x^{4} - 3 x + 23 = 4

What are the solutions to the equation x^4-2x^3+2x^2-8x-8=0 ?
The solutions to the equation x^4-2x^3+2x^2-8x-8=0 are x\approx-0.73205…,x\approx 2.73205…
Find the zeros of x^4-2x^3+2x^2-8x-8=0
The zeros of x^4-2x^3+2x^2-8x-8=0 are x\approx-0.73205…,x\approx 2.73205…