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

The solutions to the equation x^4+4x^3+x^2+2x+2=0 are x\approx-0.69173…,x\approx-3.83989…

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

The zeros of x^4+4x^3+x^2+2x+2=0 are x\approx-0.69173…,x\approx-3.83989…

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

x \approx - 0.69173 \dots, x \approx - 3.83989 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx - 0.69173 \dots

Apply long division:

\frac{x ^{4} + 4 x ^{3} + x ^{2} + 2 x + 2}{x + 0.69173 \dots} = x^{3} + 3.30826 \dots x^{2} - 1.28844 \dots x + 2.89126 \dots

x^{3} + 3.30826 \dots x^{2} - 1.28844 \dots x + 2.89126 \dots \approx 0

Find one solution for

x^{3} + 3.30826 \dots x^{2} - 1.28844 \dots x + 2.89126 \dots = 0

using Newton-Raphson:

x \approx - 3.83989 \dots

Apply long division:

\frac{x ^{3} + 3.30826 \dots x ^{2} - 1.28844 \dots x + 2.89126 \dots}{x + 3.83989 \dots} = x^{2} - 0.53163 \dots x + 0.75295 \dots

x^{2} - 0.53163 \dots x + 0.75295 \dots \approx 0

Find one solution for

x^{2} - 0.53163 \dots x + 0.75295 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 0.69173 \dots, x \approx - 3.83989 \dots

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

x (x + 1) (x^{2} - 36) = 0

x^{3} - 3 x^{2} - 50 = 0

72 x^{4} - x^{2} - 1 = 0

(1 + x)^{5} = 1.24

What are the solutions to the equation x^4+4x^3+x^2+2x+2=0 ?
The solutions to the equation x^4+4x^3+x^2+2x+2=0 are x\approx-0.69173…,x\approx-3.83989…
Find the zeros of x^4+4x^3+x^2+2x+2=0
The zeros of x^4+4x^3+x^2+2x+2=0 are x\approx-0.69173…,x\approx-3.83989…