What are the solutions to the equation x^3-6x^2+1=0 ?

The solutions to the equation x^3-6x^2+1=0 are x\approx-0.39542…,x\approx 0.42346…,x\approx 5.97196…

Find the zeros of x^3-6x^2+1=0

The zeros of x^3-6x^2+1=0 are x\approx-0.39542…,x\approx 0.42346…,x\approx 5.97196…

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

x \approx - 0.39542 \dots, x \approx 0.42346 \dots, x \approx 5.97196 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx - 0.39542 \dots

Apply long division:

\frac{x ^{3} - 6 x ^{2} + 1}{x + 0.39542 \dots} = x^{2} - 6.39542 \dots x + 2.52891 \dots

x^{2} - 6.39542 \dots x + 2.52891 \dots \approx 0

Find one solution for

x^{2} - 6.39542 \dots x + 2.52891 \dots = 0

using Newton-Raphson:

x \approx 0.42346 \dots

Apply long division:

\frac{x ^{2} - 6.39542 \dots x + 2.52891 \dots}{x - 0.42346 \dots} = x - 5.97196 \dots

x - 5.97196 \dots \approx 0

x \approx 5.97196 \dots

The solutions are

x \approx - 0.39542 \dots, x \approx 0.42346 \dots, x \approx 5.97196 \dots

4 x^{3} - 3 x = \frac{1}{2}

x^{4} - 16 x^{2} + 16 = 0

(x + 1)^{4} + 1 = 0

35 = (1 + x)^{4}

234514 x^{3} - 746760 x + 395221 = 0

What are the solutions to the equation x^3-6x^2+1=0 ?
The solutions to the equation x^3-6x^2+1=0 are x\approx-0.39542…,x\approx 0.42346…,x\approx 5.97196…
Find the zeros of x^3-6x^2+1=0
The zeros of x^3-6x^2+1=0 are x\approx-0.39542…,x\approx 0.42346…,x\approx 5.97196…