What are the solutions to the equation 3x^4-4x^3-12x^2-4=0 ?

The solutions to the equation 3x^4-4x^3-12x^2-4=0 are x\approx-1.56664…,x\approx 2.81440…

Find the zeros of 3x^4-4x^3-12x^2-4=0

The zeros of 3x^4-4x^3-12x^2-4=0 are x\approx-1.56664…,x\approx 2.81440…

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3 x^{4} - 4 x^{3} - 12 x^{2} - 4 = 0

x \approx - 1.56664 \dots, x \approx 2.81440 \dots

Solution steps

3 x^{4} - 4 x^{3} - 12 x^{2} - 4 = 0

Find one solution for

3 x^{4} - 4 x^{3} - 12 x^{2} - 4 = 0

using Newton-Raphson:

x \approx - 1.56664 \dots

Apply long division:

\frac{3 x ^{4} - 4 x ^{3} - 12 x ^{2} - 4}{x + 1.56664 \dots} = 3 x^{3} - 8.69994 \dots x^{2} + 1.62973 \dots x - 2.55322 \dots

3 x^{3} - 8.69994 \dots x^{2} + 1.62973 \dots x - 2.55322 \dots \approx 0

Find one solution for

3 x^{3} - 8.69994 \dots x^{2} + 1.62973 \dots x - 2.55322 \dots = 0

using Newton-Raphson:

x \approx 2.81440 \dots

Apply long division:

\frac{3 x ^{3} - 8.69994 \dots x ^{2} + 1.62973 \dots x - 2.55322 \dots}{x - 2.81440 \dots} = 3 x^{2} - 0.25672 \dots x + 0.90719 \dots

3 x^{2} - 0.25672 \dots x + 0.90719 \dots \approx 0

Find one solution for

3 x^{2} - 0.25672 \dots x + 0.90719 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 1.56664 \dots, x \approx 2.81440 \dots

6 x^{3} + x^{2} - 24 x - 4 = 0

x, x^{3} + y^{3} = 27

x^{3} + 6 x^{2} - 81 = 0

x, x^{3} + y^{3} = 18

x, x^{3} = \frac{y}{2}

What are the solutions to the equation 3x^4-4x^3-12x^2-4=0 ?
The solutions to the equation 3x^4-4x^3-12x^2-4=0 are x\approx-1.56664…,x\approx 2.81440…
Find the zeros of 3x^4-4x^3-12x^2-4=0
The zeros of 3x^4-4x^3-12x^2-4=0 are x\approx-1.56664…,x\approx 2.81440…