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

The solutions to the equation 3x^4-8x^3+2=0 are x\approx 0.69688…,x\approx 2.63002…

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

The zeros of 3x^4-8x^3+2=0 are x\approx 0.69688…,x\approx 2.63002…

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

x \approx 0.69688 \dots, x \approx 2.63002 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.69688 \dots

Apply long division:

\frac{3 x ^{4} - 8 x ^{3} + 2}{x - 0.69688 \dots} = 3 x^{3} - 5.90933 \dots x^{2} - 4.11815 \dots x - 2.86989 \dots

3 x^{3} - 5.90933 \dots x^{2} - 4.11815 \dots x - 2.86989 \dots \approx 0

Find one solution for

3 x^{3} - 5.90933 \dots x^{2} - 4.11815 \dots x - 2.86989 \dots = 0

using Newton-Raphson:

x \approx 2.63002 \dots

Apply long division:

\frac{3 x ^{3} - 5.90933 \dots x ^{2} - 4.11815 \dots x - 2.86989 \dots}{x - 2.63002 \dots} = 3 x^{2} + 1.98072 \dots x + 1.09120 \dots

3 x^{2} + 1.98072 \dots x + 1.09120 \dots \approx 0

Find one solution for

3 x^{2} + 1.98072 \dots x + 1.09120 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.69688 \dots, x \approx 2.63002 \dots

- 2 x^{4} + 2 = 0

12 x - 4 x^{3} = 0

x^{4} - 10 x^{2} - 20 x - 16 = 0

x^{4} + 2 x^{3} - 10 x^{2} - 18 x + 9 = 0

x^{4} = (x - 20)^{2}

What are the solutions to the equation 3x^4-8x^3+2=0 ?
The solutions to the equation 3x^4-8x^3+2=0 are x\approx 0.69688…,x\approx 2.63002…
Find the zeros of 3x^4-8x^3+2=0
The zeros of 3x^4-8x^3+2=0 are x\approx 0.69688…,x\approx 2.63002…