What are the solutions to the equation 2(x^3+3x^2+12x+4)=0 ?

The solutions to the equation 2(x^3+3x^2+12x+4)=0 are x\approx-0.36216…

Find the zeros of 2(x^3+3x^2+12x+4)=0

The zeros of 2(x^3+3x^2+12x+4)=0 are x\approx-0.36216…

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2 (x^{3} + 3 x^{2} + 12 x + 4) = 0

x \approx - 0.36216 \dots

Solution steps

2 (x^{3} + 3 x^{2} + 12 x + 4) = 0

Expand

2 (x^{3} + 3 x^{2} + 12 x + 4) : 2 x^{3} + 6 x^{2} + 24 x + 8

2 x^{3} + 6 x^{2} + 24 x + 8 = 0

Find one solution for

2 x^{3} + 6 x^{2} + 24 x + 8 = 0

using Newton-Raphson:

x \approx - 0.36216 \dots

Apply long division:

\frac{2 x ^{3} + 6 x ^{2} + 24 x + 8}{x + 0.36216 \dots} = 2 x^{2} + 5.27566 \dots x + 22.08933 \dots

2 x^{2} + 5.27566 \dots x + 22.08933 \dots \approx 0

Find one solution for

2 x^{2} + 5.27566 \dots x + 22.08933 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 0.36216 \dots

2 x^{4} + x^{3} + 3 x^{2} + 5 x + 10 = 0

x^{4} + 12 x^{3} + 12 x^{2} + 12 x + 11 = 0

x^{4} - x^{2} + 9 = 0

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

\frac{1}{3} x^{3} = 0

What are the solutions to the equation 2(x^3+3x^2+12x+4)=0 ?
The solutions to the equation 2(x^3+3x^2+12x+4)=0 are x\approx-0.36216…
Find the zeros of 2(x^3+3x^2+12x+4)=0
The zeros of 2(x^3+3x^2+12x+4)=0 are x\approx-0.36216…