What are the solutions to the equation 12x^3-9x+2=0 ?

The solutions to the equation 12x^3-9x+2=0 are x\approx 0.24085…,x\approx 0.72010…,x\approx-0.96095…

Find the zeros of 12x^3-9x+2=0

The zeros of 12x^3-9x+2=0 are x\approx 0.24085…,x\approx 0.72010…,x\approx-0.96095…

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12 x^{3} - 9 x + 2 = 0

x \approx 0.24085 \dots, x \approx 0.72010 \dots, x \approx - 0.96095 \dots

Solution steps

12 x^{3} - 9 x + 2 = 0

Find one solution for

12 x^{3} - 9 x + 2 = 0

using Newton-Raphson:

x \approx 0.24085 \dots

Apply long division:

\frac{12 x ^{3} - 9 x + 2}{x - 0.24085 \dots} = 12 x^{2} + 2.89021 \dots x - 8.30388 \dots

12 x^{2} + 2.89021 \dots x - 8.30388 \dots \approx 0

Find one solution for

12 x^{2} + 2.89021 \dots x - 8.30388 \dots = 0

using Newton-Raphson:

x \approx 0.72010 \dots

Apply long division:

\frac{12 x ^{2} + 2.89021 \dots x - 8.30388 \dots}{x - 0.72010 \dots} = 12 x + 11.53148 \dots

12 x + 11.53148 \dots \approx 0

x \approx - 0.96095 \dots

The solutions are

x \approx 0.24085 \dots, x \approx 0.72010 \dots, x \approx - 0.96095 \dots

3 x^{3} + x^{2} - 20 x + 12 = 0

4 (x^{6} + 5) = 2 x + 10

y, u = y^{3}

(1 + x)^{5} = 4

\frac{8}{125} = x^{3}

What are the solutions to the equation 12x^3-9x+2=0 ?
The solutions to the equation 12x^3-9x+2=0 are x\approx 0.24085…,x\approx 0.72010…,x\approx-0.96095…
Find the zeros of 12x^3-9x+2=0
The zeros of 12x^3-9x+2=0 are x\approx 0.24085…,x\approx 0.72010…,x\approx-0.96095…