What are the solutions to the equation 0=(a+1)^3+3a^2 ?

The solutions to the equation 0=(a+1)^3+3a^2 are a\approx-5.48641…

Find the zeros of 0=(a+1)^3+3a^2

The zeros of 0=(a+1)^3+3a^2 are a\approx-5.48641…

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0 = (a + 1)^{3} + 3 a^{2}

a \approx - 5.48641 \dots

Solution steps

0 = (a + 1)^{3} + 3 a^{2}

Expand

(a + 1)^{3} + 3 a^{2} : a^{3} + 6 a^{2} + 3 a + 1

0 = a^{3} + 6 a^{2} + 3 a + 1

Switch sides

a^{3} + 6 a^{2} + 3 a + 1 = 0

Find one solution for

a^{3} + 6 a^{2} + 3 a + 1 = 0

using Newton-Raphson:

a \approx - 5.48641 \dots

Apply long division:

\frac{a ^{3} + 6 a ^{2} + 3 a + 1}{a + 5.48641 \dots} = a^{2} + 0.51358 \dots a + 0.18226 \dots

a^{2} + 0.51358 \dots a + 0.18226 \dots \approx 0

Find one solution for

a^{2} + 0.51358 \dots a + 0.18226 \dots = 0

using Newton-Raphson:

No Solution for

a \in R

The solution is

a \approx - 5.48641 \dots

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

0 = x^{5} - 3 x^{3} + 8 x^{2} - 24

2 x^{4} - 13 x^{3} + 28 x^{2} - 23 x + 6 = 0

x^{4} - 64 x^{2} = 0

x^{6} - 6 x^{3} - 16 = 0

What are the solutions to the equation 0=(a+1)^3+3a^2 ?
The solutions to the equation 0=(a+1)^3+3a^2 are a\approx-5.48641…
Find the zeros of 0=(a+1)^3+3a^2
The zeros of 0=(a+1)^3+3a^2 are a\approx-5.48641…