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

The solutions to the equation 0=3x^4+4x^3-12x^2+12 are x\approx-0.95786…,x\approx-2.63328…

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

The zeros of 0=3x^4+4x^3-12x^2+12 are x\approx-0.95786…,x\approx-2.63328…

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

x \approx - 0.95786 \dots, x \approx - 2.63328 \dots

Solution steps

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

Switch sides

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

Find one solution for

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

using Newton-Raphson:

x \approx - 0.95786 \dots

Apply long division:

\frac{3 x ^{4} + 4 x ^{3} - 12 x ^{2} + 12}{x + 0.95786 \dots} = 3 x^{3} + 1.12640 \dots x^{2} - 13.07894 \dots x + 12.52786 \dots

3 x^{3} + 1.12640 \dots x^{2} - 13.07894 \dots x + 12.52786 \dots \approx 0

Find one solution for

3 x^{3} + 1.12640 \dots x^{2} - 13.07894 \dots x + 12.52786 \dots = 0

using Newton-Raphson:

x \approx - 2.63328 \dots

Apply long division:

\frac{3 x ^{3} + 1.12640 \dots x ^{2} - 13.07894 \dots x + 12.52786 \dots}{x + 2.63328 \dots} = 3 x^{2} - 6.77345 \dots x + 4.75750 \dots

3 x^{2} - 6.77345 \dots x + 4.75750 \dots \approx 0

Find one solution for

3 x^{2} - 6.77345 \dots x + 4.75750 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 0.95786 \dots, x \approx - 2.63328 \dots

15 x^{4} + 7 x^{2} - 2 = 0

(x + 5) \cdot (x - 5)^{2} x = 3

9 a^{3} = 16 a

x, x^{3} - 15 x - 126 = 0

x^{3} - 5 x^{2} + 3 x = \frac{1}{2}

What are the solutions to the equation 0=3x^4+4x^3-12x^2+12 ?
The solutions to the equation 0=3x^4+4x^3-12x^2+12 are x\approx-0.95786…,x\approx-2.63328…
Find the zeros of 0=3x^4+4x^3-12x^2+12
The zeros of 0=3x^4+4x^3-12x^2+12 are x\approx-0.95786…,x\approx-2.63328…