What are the solutions to the equation 6x^4-8x^3+1=0 ?

The solutions to the equation 6x^4-8x^3+1=0 are x\approx 1.24748…,x\approx 0.61427…

Find the zeros of 6x^4-8x^3+1=0

The zeros of 6x^4-8x^3+1=0 are x\approx 1.24748…,x\approx 0.61427…

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6 x^{4} - 8 x^{3} + 1 = 0

x \approx 1.24748 \dots, x \approx 0.61427 \dots

Solution steps

6 x^{4} - 8 x^{3} + 1 = 0

Find one solution for

6 x^{4} - 8 x^{3} + 1 = 0

using Newton-Raphson:

x \approx 1.24748 \dots

Apply long division:

\frac{6 x ^{4} - 8 x ^{3} + 1}{x - 1.24748 \dots} = 6 x^{3} - 0.51510 \dots x^{2} - 0.64258 \dots x - 0.80161 \dots

6 x^{3} - 0.51510 \dots x^{2} - 0.64258 \dots x - 0.80161 \dots \approx 0

Find one solution for

6 x^{3} - 0.51510 \dots x^{2} - 0.64258 \dots x - 0.80161 \dots = 0

using Newton-Raphson:

x \approx 0.61427 \dots

Apply long division:

\frac{6 x ^{3} - 0.51510 \dots x ^{2} - 0.64258 \dots x - 0.80161 \dots}{x - 0.61427 \dots} = 6 x^{2} + 3.17052 \dots x + 1.30498 \dots

6 x^{2} + 3.17052 \dots x + 1.30498 \dots \approx 0

Find one solution for

6 x^{2} + 3.17052 \dots x + 1.30498 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1.24748 \dots, x \approx 0.61427 \dots

x^{3} - 6 x^{2} - 3 x + 6 = 0

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

z^{3} = 1 - i

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

y^{3} + 8 = 0

What are the solutions to the equation 6x^4-8x^3+1=0 ?
The solutions to the equation 6x^4-8x^3+1=0 are x\approx 1.24748…,x\approx 0.61427…
Find the zeros of 6x^4-8x^3+1=0
The zeros of 6x^4-8x^3+1=0 are x\approx 1.24748…,x\approx 0.61427…