What are the solutions to the equation x^5-3x+1=0 ?

The solutions to the equation x^5-3x+1=0 are x\approx 0.33473…,x\approx 1.21464…,x\approx-1.38879…

Find the zeros of x^5-3x+1=0

The zeros of x^5-3x+1=0 are x\approx 0.33473…,x\approx 1.21464…,x\approx-1.38879…

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x^{5} - 3 x + 1 = 0

x \approx 0.33473 \dots, x \approx 1.21464 \dots, x \approx - 1.38879 \dots

Solution steps

x^{5} - 3 x + 1 = 0

Find one solution for

x^{5} - 3 x + 1 = 0

using Newton-Raphson:

x \approx 0.33473 \dots

Apply long division:

\frac{x ^{5} - 3 x + 1}{x - 0.33473 \dots} = x^{4} + 0.33473 \dots x^{3} + 0.11204 \dots x^{2} + 0.03750 \dots x - 2.98744 \dots

x^{4} + 0.33473 \dots x^{3} + 0.11204 \dots x^{2} + 0.03750 \dots x - 2.98744 \dots \approx 0

Find one solution for

x^{4} + 0.33473 \dots x^{3} + 0.11204 \dots x^{2} + 0.03750 \dots x - 2.98744 \dots = 0

using Newton-Raphson:

x \approx 1.21464 \dots

Apply long division:

\frac{x ^{4} + 0.33473 \dots x ^{3} + 0.11204 \dots x ^{2} + 0.03750 \dots x - 2.98744 \dots}{x - 1.21464 \dots} = x^{3} + 1.54938 \dots x^{2} + 1.99400 \dots x + 2.45951 \dots

x^{3} + 1.54938 \dots x^{2} + 1.99400 \dots x + 2.45951 \dots \approx 0

Find one solution for

x^{3} + 1.54938 \dots x^{2} + 1.99400 \dots x + 2.45951 \dots = 0

using Newton-Raphson:

x \approx - 1.38879 \dots

Apply long division:

\frac{x ^{3} + 1.54938 \dots x ^{2} + 1.99400 \dots x + 2.45951 \dots}{x + 1.38879 \dots} = x^{2} + 0.16059 \dots x + 1.77097 \dots

x^{2} + 0.16059 \dots x + 1.77097 \dots \approx 0

Find one solution for

x^{2} + 0.16059 \dots x + 1.77097 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.33473 \dots, x \approx 1.21464 \dots, x \approx - 1.38879 \dots

- 2 (9 x^{2} - 49) (x^{2} - 5) = 0

x^{4} - 7 x^{3} + 12 x^{2} + 4 x - 16 = 0

x^{4} - 38 x^{2} + 72 = 0

- 9 x^{4} - 46 x^{2} + 5 = 0

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

What are the solutions to the equation x^5-3x+1=0 ?
The solutions to the equation x^5-3x+1=0 are x\approx 0.33473…,x\approx 1.21464…,x\approx-1.38879…
Find the zeros of x^5-3x+1=0
The zeros of x^5-3x+1=0 are x\approx 0.33473…,x\approx 1.21464…,x\approx-1.38879…