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

The solutions to the equation 12x^3=-3x^2-12 are x\approx-1.09066…

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

The zeros of 12x^3=-3x^2-12 are x\approx-1.09066…

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

x \approx - 1.09066 \dots

Solution steps

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

Move

12

to the left side

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

Move

3 x^{2}

to the left side

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

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

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

Find one solution for

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

using Newton-Raphson:

x \approx - 1.09066 \dots

Apply long division:

\frac{12 x ^{3} + 3 x ^{2} + 12}{x + 1.09066 \dots} = 12 x^{2} - 10.08792 \dots x + 11.00250 \dots

12 x^{2} - 10.08792 \dots x + 11.00250 \dots \approx 0

Find one solution for

12 x^{2} - 10.08792 \dots x + 11.00250 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 1.09066 \dots

\frac{256}{3125} x^{5} = 1

4 c^{3} + 24 c^{2} - 64 c = 0

x^{2} - 6 x = 2 x^{2} x

- a^{3} + 6 a^{2} + 15 a + 8 = 0

3 = n^{3} - 3 n^{2} + n

What are the solutions to the equation 12x^3=-3x^2-12 ?
The solutions to the equation 12x^3=-3x^2-12 are x\approx-1.09066…
Find the zeros of 12x^3=-3x^2-12
The zeros of 12x^3=-3x^2-12 are x\approx-1.09066…