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

The solutions to the equation 4x^3-6x+1=0 are x\approx 0.16993…,x\approx 1.13090…,x\approx-1.30083…

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

The zeros of 4x^3-6x+1=0 are x\approx 0.16993…,x\approx 1.13090…,x\approx-1.30083…

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

x \approx 0.16993 \dots, x \approx 1.13090 \dots, x \approx - 1.30083 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.16993 \dots

Apply long division:

\frac{4 x ^{3} - 6 x + 1}{x - 0.16993 \dots} = 4 x^{2} + 0.67975 \dots x - 5.88448 \dots

4 x^{2} + 0.67975 \dots x - 5.88448 \dots \approx 0

Find one solution for

4 x^{2} + 0.67975 \dots x - 5.88448 \dots = 0

using Newton-Raphson:

x \approx 1.13090 \dots

Apply long division:

\frac{4 x ^{2} + 0.67975 \dots x - 5.88448 \dots}{x - 1.13090 \dots} = 4 x + 5.20335 \dots

4 x + 5.20335 \dots \approx 0

x \approx - 1.30083 \dots

The solutions are

x \approx 0.16993 \dots, x \approx 1.13090 \dots, x \approx - 1.30083 \dots

125 x^{3} = 64

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

8 y^{3} - 125 = 0

(x + 6)^{4} = 0

4 x^{3} - 6 x^{2} + 1 = 0

What are the solutions to the equation 4x^3-6x+1=0 ?
The solutions to the equation 4x^3-6x+1=0 are x\approx 0.16993…,x\approx 1.13090…,x\approx-1.30083…
Find the zeros of 4x^3-6x+1=0
The zeros of 4x^3-6x+1=0 are x\approx 0.16993…,x\approx 1.13090…,x\approx-1.30083…