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

The solutions to the equation x^4-2x^3+x^2-2=0 are x\approx-0.79004…,x\approx 1.79004…

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

The zeros of x^4-2x^3+x^2-2=0 are x\approx-0.79004…,x\approx 1.79004…

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

x \approx - 0.79004 \dots, x \approx 1.79004 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx - 0.79004 \dots

Apply long division:

\frac{x ^{4} - 2 x ^{3} + x ^{2} - 2}{x + 0.79004 \dots} = x^{3} - 2.79004 \dots x^{2} + 3.20425 \dots x - 2.53150 \dots

x^{3} - 2.79004 \dots x^{2} + 3.20425 \dots x - 2.53150 \dots \approx 0

Find one solution for

x^{3} - 2.79004 \dots x^{2} + 3.20425 \dots x - 2.53150 \dots = 0

using Newton-Raphson:

x \approx 1.79004 \dots

Apply long division:

\frac{x ^{3} - 2.79004 \dots x ^{2} + 3.20425 \dots x - 2.53150 \dots}{x - 1.79004 \dots} = x^{2} - x + 1.41421 \dots

x^{2} - x + 1.41421 \dots \approx 0

Find one solution for

x^{2} - x + 1.41421 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 0.79004 \dots, x \approx 1.79004 \dots

x^{6} - 7 x^{3} + 10 = 0

4 x^{3} = 16 x^{2} - 48 x

- x^{3} + 8 x^{2} - 13 x + 2 = 0

r^{4} - r + 1 = 0

x^{3} - 5 x^{2} - 8 x = 12

What are the solutions to the equation x^4-2x^3+x^2-2=0 ?
The solutions to the equation x^4-2x^3+x^2-2=0 are x\approx-0.79004…,x\approx 1.79004…
Find the zeros of x^4-2x^3+x^2-2=0
The zeros of x^4-2x^3+x^2-2=0 are x\approx-0.79004…,x\approx 1.79004…