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

The solutions to the equation u^3+u^2+1=0 are u\approx-1.46557…

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

The zeros of u^3+u^2+1=0 are u\approx-1.46557…

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

u \approx - 1.46557 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

u \approx - 1.46557 \dots

Apply long division:

\frac{u ^{3} + u ^{2} + 1}{u + 1.46557 \dots} = u^{2} - 0.46557 \dots u + 0.68232 \dots

u^{2} - 0.46557 \dots u + 0.68232 \dots \approx 0

Find one solution for

u^{2} - 0.46557 \dots u + 0.68232 \dots = 0

using Newton-Raphson:

No Solution for

u \in R

The solution is

u \approx - 1.46557 \dots

x^{3} - 14 x^{2} + 40 x = 0

31 = x^{4}

x^{3} + x^{2} = 150

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

x^{3} + 7 x^{2} - 2 x - 40 = 0

What are the solutions to the equation u^3+u^2+1=0 ?
The solutions to the equation u^3+u^2+1=0 are u\approx-1.46557…
Find the zeros of u^3+u^2+1=0
The zeros of u^3+u^2+1=0 are u\approx-1.46557…