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

The solutions to the equation x^5-5x+3=0 are x\approx 1.27568…,x\approx 0.61803…,x\approx-1.61803…

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

The zeros of x^5-5x+3=0 are x\approx 1.27568…,x\approx 0.61803…,x\approx-1.61803…

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

x \approx 1.27568 \dots, x \approx 0.61803 \dots, x \approx - 1.61803 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx 1.27568 \dots

Apply long division:

\frac{x ^{5} - 5 x + 3}{x - 1.27568 \dots} = x^{4} + 1.27568 \dots x^{3} + 1.62736 \dots x^{2} + 2.07600 \dots x - 2.35168 \dots

x^{4} + 1.27568 \dots x^{3} + 1.62736 \dots x^{2} + 2.07600 \dots x - 2.35168 \dots \approx 0

Find one solution for

x^{4} + 1.27568 \dots x^{3} + 1.62736 \dots x^{2} + 2.07600 \dots x - 2.35168 \dots = 0

using Newton-Raphson:

x \approx 0.61803 \dots

Apply long division:

\frac{x ^{4} + 1.27568 \dots x ^{3} + 1.62736 \dots x ^{2} + 2.07600 \dots x - 2.35168 \dots}{x - 0.61803 \dots} = x^{3} + 1.89371 \dots x^{2} + 2.79774 \dots x + 3.80510 \dots

x^{3} + 1.89371 \dots x^{2} + 2.79774 \dots x + 3.80510 \dots \approx 0

Find one solution for

x^{3} + 1.89371 \dots x^{2} + 2.79774 \dots x + 3.80510 \dots = 0

using Newton-Raphson:

x \approx - 1.61803 \dots

Apply long division:

\frac{x ^{3} + 1.89371 \dots x ^{2} + 2.79774 \dots x + 3.80510 \dots}{x + 1.61803 \dots} = x^{2} + 0.27568 \dots x + 2.35168 \dots

x^{2} + 0.27568 \dots x + 2.35168 \dots \approx 0

Find one solution for

x^{2} + 0.27568 \dots x + 2.35168 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1.27568 \dots, x \approx 0.61803 \dots, x \approx - 1.61803 \dots

(z^{2} + 25)^{2} = 0

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

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

8 x^{4} = x

x^{5} + (2 - x)^{5} = 82

What are the solutions to the equation x^5-5x+3=0 ?
The solutions to the equation x^5-5x+3=0 are x\approx 1.27568…,x\approx 0.61803…,x\approx-1.61803…
Find the zeros of x^5-5x+3=0
The zeros of x^5-5x+3=0 are x\approx 1.27568…,x\approx 0.61803…,x\approx-1.61803…