What are the solutions to the equation 3x^4+4x^3-12x^2+8=0 ?

The solutions to the equation 3x^4+4x^3-12x^2+8=0 are x\approx-0.77563…,x\approx-2.68523…

Find the zeros of 3x^4+4x^3-12x^2+8=0

The zeros of 3x^4+4x^3-12x^2+8=0 are x\approx-0.77563…,x\approx-2.68523…

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3 x^{4} + 4 x^{3} - 12 x^{2} + 8 = 0

x \approx - 0.77563 \dots, x \approx - 2.68523 \dots

Solution steps

3 x^{4} + 4 x^{3} - 12 x^{2} + 8 = 0

Find one solution for

3 x^{4} + 4 x^{3} - 12 x^{2} + 8 = 0

using Newton-Raphson:

x \approx - 0.77563 \dots

Apply long division:

\frac{3 x ^{4} + 4 x ^{3} - 12 x ^{2} + 8}{x + 0.77563 \dots} = 3 x^{3} + 1.67309 \dots x^{2} - 13.29771 \dots x + 10.31415 \dots

3 x^{3} + 1.67309 \dots x^{2} - 13.29771 \dots x + 10.31415 \dots \approx 0

Find one solution for

3 x^{3} + 1.67309 \dots x^{2} - 13.29771 \dots x + 10.31415 \dots = 0

using Newton-Raphson:

x \approx - 2.68523 \dots

Apply long division:

\frac{3 x ^{3} + 1.67309 \dots x ^{2} - 13.29771 \dots x + 10.31415 \dots}{x + 2.68523 \dots} = 3 x^{2} - 6.38260 \dots x + 3.84106 \dots

3 x^{2} - 6.38260 \dots x + 3.84106 \dots \approx 0

Find one solution for

3 x^{2} - 6.38260 \dots x + 3.84106 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 0.77563 \dots, x \approx - 2.68523 \dots

25 x^{4} = 61 x^{2} - 36

c^{4} = 3

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

4 x (x^{2} - 1) = 0

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

What are the solutions to the equation 3x^4+4x^3-12x^2+8=0 ?
The solutions to the equation 3x^4+4x^3-12x^2+8=0 are x\approx-0.77563…,x\approx-2.68523…
Find the zeros of 3x^4+4x^3-12x^2+8=0
The zeros of 3x^4+4x^3-12x^2+8=0 are x\approx-0.77563…,x\approx-2.68523…