What are the solutions to the equation x^5+10x^3+20x-4=0 ?

The solutions to the equation x^5+10x^3+20x-4=0 are x\approx 0.19620…

Find the zeros of x^5+10x^3+20x-4=0

The zeros of x^5+10x^3+20x-4=0 are x\approx 0.19620…

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x^{5} + 10 x^{3} + 20 x - 4 = 0

x \approx 0.19620 \dots

Solution steps

x^{5} + 10 x^{3} + 20 x - 4 = 0

Find one solution for

x^{5} + 10 x^{3} + 20 x - 4 = 0

using Newton-Raphson:

x \approx 0.19620 \dots

Apply long division:

\frac{x ^{5} + 10 x ^{3} + 20 x - 4}{x - 0.19620 \dots} = x^{4} + 0.19620 \dots x^{3} + 10.03849 \dots x^{2} + 1.96964 \dots x + 20.38646 \dots

x^{4} + 0.19620 \dots x^{3} + 10.03849 \dots x^{2} + 1.96964 \dots x + 20.38646 \dots \approx 0

Find one solution for

x^{4} + 0.19620 \dots x^{3} + 10.03849 \dots x^{2} + 1.96964 \dots x + 20.38646 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.19620 \dots

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

3 x^{3} - 2 x^{2} + 12 x - 8 = 0

x^{4} - 4 x^{3} + 2 x^{2} - 5 x + 7 = 0

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

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

What are the solutions to the equation x^5+10x^3+20x-4=0 ?
The solutions to the equation x^5+10x^3+20x-4=0 are x\approx 0.19620…
Find the zeros of x^5+10x^3+20x-4=0
The zeros of x^5+10x^3+20x-4=0 are x\approx 0.19620…