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

The solutions to the equation 0=4x^3+2x-12 are x\approx 1.32695…

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

The zeros of 0=4x^3+2x-12 are x\approx 1.32695…

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

x \approx 1.32695 \dots

Solution steps

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

Switch sides

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

Find one solution for

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

using Newton-Raphson:

x \approx 1.32695 \dots

Apply long division:

\frac{4 x ^{3} + 2 x - 12}{x - 1.32695 \dots} = 4 x^{2} + 5.30782 \dots x + 9.04325 \dots

4 x^{2} + 5.30782 \dots x + 9.04325 \dots \approx 0

Find one solution for

4 x^{2} + 5.30782 \dots x + 9.04325 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.32695 \dots

64 x = x^{4}

6 x^{3} - 11 x^{2} - 9 x - 1 = 0

30 x^{4} - 120 x^{3} = 0

4 x^{3} - 12 x^{2} - 9 x - 1 = 0

2 x^{3} + 3 x^{2} - 12 x + 1 = 0

What are the solutions to the equation 0=4x^3+2x-12 ?
The solutions to the equation 0=4x^3+2x-12 are x\approx 1.32695…
Find the zeros of 0=4x^3+2x-12
The zeros of 0=4x^3+2x-12 are x\approx 1.32695…