What are the solutions to the equation x^1+2x^2-x^3=4 ?

The solutions to the equation x^1+2x^2-x^3=4 are x\approx-1.26953…

Find the zeros of x^1+2x^2-x^3=4

The zeros of x^1+2x^2-x^3=4 are x\approx-1.26953…

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

x \approx - 1.26953 \dots

Solution steps

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

Refine

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

Move

4

to the left side

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

Write in the standard form

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

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

Find one solution for

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

using Newton-Raphson:

x \approx - 1.26953 \dots

Apply long division:

\frac{- x ^{3} + 2 x ^{2} + x - 4}{x + 1.26953 \dots} = - x^{2} + 3.26953 \dots x - 3.15077 \dots

- x^{2} + 3.26953 \dots x - 3.15077 \dots \approx 0

Find one solution for

- x^{2} + 3.26953 \dots x - 3.15077 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 1.26953 \dots

3 x^{3} - 10 x^{2} + 8 x = 0

(x - 2)^{5} = 0

2 x^{3} - 9 x^{2} - x + 2 = 0

(\frac{2 x}{6})^{3} = 8

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

What are the solutions to the equation x^1+2x^2-x^3=4 ?
The solutions to the equation x^1+2x^2-x^3=4 are x\approx-1.26953…
Find the zeros of x^1+2x^2-x^3=4
The zeros of x^1+2x^2-x^3=4 are x\approx-1.26953…