What are the solutions to the equation 4x^3-24x+1=0 ?

The solutions to the equation 4x^3-24x+1=0 are x\approx 0.04167…,x\approx 2.42838…,x\approx-2.47006…

Find the zeros of 4x^3-24x+1=0

The zeros of 4x^3-24x+1=0 are x\approx 0.04167…,x\approx 2.42838…,x\approx-2.47006…

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4 x^{3} - 24 x + 1 = 0

x \approx 0.04167 \dots, x \approx 2.42838 \dots, x \approx - 2.47006 \dots

Solution steps

4 x^{3} - 24 x + 1 = 0

Find one solution for

4 x^{3} - 24 x + 1 = 0

using Newton-Raphson:

x \approx 0.04167 \dots

Apply long division:

\frac{4 x ^{3} - 24 x + 1}{x - 0.04167 \dots} = 4 x^{2} + 0.16671 \dots x - 23.99305 \dots

4 x^{2} + 0.16671 \dots x - 23.99305 \dots \approx 0

Find one solution for

4 x^{2} + 0.16671 \dots x - 23.99305 \dots = 0

using Newton-Raphson:

x \approx 2.42838 \dots

Apply long division:

\frac{4 x ^{2} + 0.16671 \dots x - 23.99305 \dots}{x - 2.42838 \dots} = 4 x + 9.88025 \dots

4 x + 9.88025 \dots \approx 0

x \approx - 2.47006 \dots

The solutions are

x \approx 0.04167 \dots, x \approx 2.42838 \dots, x \approx - 2.47006 \dots

x (x - 1)^{2} = 1

x^{8} + 8 x^{4} + 16 = 0

x^{2015} = x^{2016}

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

2 x^{4} - 3 x^{3} + 12 x^{2} - 16 x + 5 = 0

What are the solutions to the equation 4x^3-24x+1=0 ?
The solutions to the equation 4x^3-24x+1=0 are x\approx 0.04167…,x\approx 2.42838…,x\approx-2.47006…
Find the zeros of 4x^3-24x+1=0
The zeros of 4x^3-24x+1=0 are x\approx 0.04167…,x\approx 2.42838…,x\approx-2.47006…