What are the solutions to the equation x^1+2x^2+x^3=-1 ?

The solutions to the equation x^1+2x^2+x^3=-1 are x\approx-1.75487…

Find the zeros of x^1+2x^2+x^3=-1

The zeros of x^1+2x^2+x^3=-1 are x\approx-1.75487…

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x^{1} + 2 x^{2} + x^{3} = - 1

x \approx - 1.75487 \dots

Solution steps

x^{1} + 2 x^{2} + x^{3} = - 1

Refine

x + 2 x^{2} + x^{3} = - 1

Move

1

to the left side

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

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

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

Find one solution for

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

using Newton-Raphson:

x \approx - 1.75487 \dots

Apply long division:

\frac{x ^{3} + 2 x ^{2} + x + 1}{x + 1.75487 \dots} = x^{2} + 0.24512 \dots x + 0.56984 \dots

x^{2} + 0.24512 \dots x + 0.56984 \dots \approx 0

Find one solution for

x^{2} + 0.24512 \dots x + 0.56984 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 1.75487 \dots

4 x^{3} - 54 x^{2} + 180 x - 125 = 0

2 k^{3} - 8 k^{2} + 2 k + 1 = 0

b^{4} - 6 b^{3} - 5 b^{2} + 42 b + 40 = 0

3 x^{3} + 13 x^{2} - 10 x = 0

x^{3} = x - 2

What are the solutions to the equation x^1+2x^2+x^3=-1 ?
The solutions to the equation x^1+2x^2+x^3=-1 are x\approx-1.75487…
Find the zeros of x^1+2x^2+x^3=-1
The zeros of x^1+2x^2+x^3=-1 are x\approx-1.75487…