What are the solutions to the equation x^5+5x^4+3x^2+x+6=0 ?

The solutions to the equation x^5+5x^4+3x^2+x+6=0 are x\approx-5.11591…

Find the zeros of x^5+5x^4+3x^2+x+6=0

The zeros of x^5+5x^4+3x^2+x+6=0 are x\approx-5.11591…

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x^{5} + 5 x^{4} + 3 x^{2} + x + 6 = 0

x \approx - 5.11591 \dots

Solution steps

x^{5} + 5 x^{4} + 3 x^{2} + x + 6 = 0

Find one solution for

x^{5} + 5 x^{4} + 3 x^{2} + x + 6 = 0

using Newton-Raphson:

x \approx - 5.11591 \dots

Apply long division:

\frac{x ^{5} + 5 x ^{4} + 3 x ^{2} + x + 6}{x + 5.11591 \dots} = x^{4} - 0.11591 \dots x^{3} + 0.59300 \dots x^{2} - 0.03377 \dots x + 1.17281 \dots

x^{4} - 0.11591 \dots x^{3} + 0.59300 \dots x^{2} - 0.03377 \dots x + 1.17281 \dots \approx 0

Find one solution for

x^{4} - 0.11591 \dots x^{3} + 0.59300 \dots x^{2} - 0.03377 \dots x + 1.17281 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 5.11591 \dots

\frac{x ^{5}}{3} = 1 0^{6}

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

r^{3} - 3 r^{2} - r + 3 = 0

x^{4} - \frac{17}{4} x^{2} + 1 = 0

x^{6} - 10 x^{3} + 21 = 0

What are the solutions to the equation x^5+5x^4+3x^2+x+6=0 ?
The solutions to the equation x^5+5x^4+3x^2+x+6=0 are x\approx-5.11591…
Find the zeros of x^5+5x^4+3x^2+x+6=0
The zeros of x^5+5x^4+3x^2+x+6=0 are x\approx-5.11591…