What are the solutions to the equation x^5-5x^3+3=0 ?

The solutions to the equation x^5-5x^3+3=0 are x\approx 2.16936…,x\approx-2.29116…,x\approx 0.89382…

Find the zeros of x^5-5x^3+3=0

The zeros of x^5-5x^3+3=0 are x\approx 2.16936…,x\approx-2.29116…,x\approx 0.89382…

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x^{5} - 5 x^{3} + 3 = 0

x \approx 2.16936 \dots, x \approx - 2.29116 \dots, x \approx 0.89382 \dots

Solution steps

x^{5} - 5 x^{3} + 3 = 0

Find one solution for

x^{5} - 5 x^{3} + 3 = 0

using Newton-Raphson:

x \approx 2.16936 \dots

Apply long division:

\frac{x ^{5} - 5 x ^{3} + 3}{x - 2.16936 \dots} = x^{4} + 2.16936 \dots x^{3} - 0.29384 \dots x^{2} - 0.63746 \dots x - 1.38289 \dots

x^{4} + 2.16936 \dots x^{3} - 0.29384 \dots x^{2} - 0.63746 \dots x - 1.38289 \dots \approx 0

Find one solution for

x^{4} + 2.16936 \dots x^{3} - 0.29384 \dots x^{2} - 0.63746 \dots x - 1.38289 \dots = 0

using Newton-Raphson:

x \approx - 2.29116 \dots

Apply long division:

\frac{x ^{4} + 2.16936 \dots x ^{3} - 0.29384 \dots x ^{2} - 0.63746 \dots x - 1.38289 \dots}{x + 2.29116 \dots} = x^{3} - 0.12179 \dots x^{2} - 0.01479 \dots x - 0.60357 \dots

x^{3} - 0.12179 \dots x^{2} - 0.01479 \dots x - 0.60357 \dots \approx 0

Find one solution for

x^{3} - 0.12179 \dots x^{2} - 0.01479 \dots x - 0.60357 \dots = 0

using Newton-Raphson:

x \approx 0.89382 \dots

Apply long division:

\frac{x ^{3} - 0.12179 \dots x ^{2} - 0.01479 \dots x - 0.60357 \dots}{x - 0.89382 \dots} = x^{2} + 0.77203 \dots x + 0.67527 \dots

x^{2} + 0.77203 \dots x + 0.67527 \dots \approx 0

Find one solution for

x^{2} + 0.77203 \dots x + 0.67527 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 2.16936 \dots, x \approx - 2.29116 \dots, x \approx 0.89382 \dots

y, 12 y^{3} - 1 y^{2} - 6 y = 0

6 x^{4} + 2 x^{2} - 8 = 0

r^{3} + r = 0

2 x^{4} - 19 x^{2} + 9 = 0

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

What are the solutions to the equation x^5-5x^3+3=0 ?
The solutions to the equation x^5-5x^3+3=0 are x\approx 2.16936…,x\approx-2.29116…,x\approx 0.89382…
Find the zeros of x^5-5x^3+3=0
The zeros of x^5-5x^3+3=0 are x\approx 2.16936…,x\approx-2.29116…,x\approx 0.89382…