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

The solutions to the equation 4x^3-8x+1=0 are x\approx 0.12600…,x\approx 1.34699…,x\approx-1.47299…

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

The zeros of 4x^3-8x+1=0 are x\approx 0.12600…,x\approx 1.34699…,x\approx-1.47299…

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

x \approx 0.12600 \dots, x \approx 1.34699 \dots, x \approx - 1.47299 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.12600 \dots

Apply long division:

\frac{4 x ^{3} - 8 x + 1}{x - 0.12600 \dots} = 4 x^{2} + 0.50400 \dots x - 7.93649 \dots

4 x^{2} + 0.50400 \dots x - 7.93649 \dots \approx 0

Find one solution for

4 x^{2} + 0.50400 \dots x - 7.93649 \dots = 0

using Newton-Raphson:

x \approx 1.34699 \dots

Apply long division:

\frac{4 x ^{2} + 0.50400 \dots x - 7.93649 \dots}{x - 1.34699 \dots} = 4 x + 5.89199 \dots

4 x + 5.89199 \dots \approx 0

x \approx - 1.47299 \dots

The solutions are

x \approx 0.12600 \dots, x \approx 1.34699 \dots, x \approx - 1.47299 \dots

2 m x^{4} + 3 n x^{4} + 10 m + 15 n

A, A^{4} t = m - R^{2}

x^{3} + 4 x

x^{3} - 23 x^{2} + 22 x = 0

9 x^{8} - 72 x^{7} = 0

What are the solutions to the equation 4x^3-8x+1=0 ?
The solutions to the equation 4x^3-8x+1=0 are x\approx 0.12600…,x\approx 1.34699…,x\approx-1.47299…
Find the zeros of 4x^3-8x+1=0
The zeros of 4x^3-8x+1=0 are x\approx 0.12600…,x\approx 1.34699…,x\approx-1.47299…