What are the solutions to the equation 1+x+3x^2+x^3=0 ?

The solutions to the equation 1+x+3x^2+x^3=0 are x\approx-2.76929…

Find the zeros of 1+x+3x^2+x^3=0

The zeros of 1+x+3x^2+x^3=0 are x\approx-2.76929…

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

x \approx - 2.76929 \dots

Solution steps

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

Write in the standard form

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

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

Find one solution for

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

using Newton-Raphson:

x \approx - 2.76929 \dots

Apply long division:

\frac{x ^{3} + 3 x ^{2} + x + 1}{x + 2.76929 \dots} = x^{2} + 0.23070 \dots x + 0.36110 \dots

x^{2} + 0.23070 \dots x + 0.36110 \dots \approx 0

Find one solution for

x^{2} + 0.23070 \dots x + 0.36110 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 2.76929 \dots

x^{5} + 30 = 0

k^{3} = 125

x^{4} + 2 x^{3} - 35 x^{2} = 0

(2 x - 3) (2 x^{2} + 5 x + 3) = 0

z^{4} + z^{2} + 1 + i = 0

What are the solutions to the equation 1+x+3x^2+x^3=0 ?
The solutions to the equation 1+x+3x^2+x^3=0 are x\approx-2.76929…
Find the zeros of 1+x+3x^2+x^3=0
The zeros of 1+x+3x^2+x^3=0 are x\approx-2.76929…