What are the solutions to the equation x^5-2x^3+x^2+2=-1 ?

The solutions to the equation x^5-2x^3+x^2+2=-1 are x\approx-1.76436…

Find the zeros of x^5-2x^3+x^2+2=-1

The zeros of x^5-2x^3+x^2+2=-1 are x\approx-1.76436…

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x^{5} - 2 x^{3} + x^{2} + 2 = - 1

x \approx - 1.76436 \dots

Solution steps

x^{5} - 2 x^{3} + x^{2} + 2 = - 1

Move

1

to the left side

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

Find one solution for

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

using Newton-Raphson:

x \approx - 1.76436 \dots

Apply long division:

\frac{x ^{5} - 2 x ^{3} + x ^{2} + 3}{x + 1.76436 \dots} = x^{4} - 1.76436 \dots x^{3} + 1.11298 \dots x^{2} - 0.96370 \dots x + 1.70032 \dots

x^{4} - 1.76436 \dots x^{3} + 1.11298 \dots x^{2} - 0.96370 \dots x + 1.70032 \dots \approx 0

Find one solution for

x^{4} - 1.76436 \dots x^{3} + 1.11298 \dots x^{2} - 0.96370 \dots x + 1.70032 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 1.76436 \dots

x^{5} + 8 x^{4} - 20 x^{3} = 0

75 x - 4.023 = 25.502 \cdot x^{3}

6 x^{4} + 11 x^{2} + 4 = 0

x^{2} (x^{2} - 16) - 49 (x^{2} - 16) = 0

v^{8} v + 4 v - 14 = - 53

What are the solutions to the equation x^5-2x^3+x^2+2=-1 ?
The solutions to the equation x^5-2x^3+x^2+2=-1 are x\approx-1.76436…
Find the zeros of x^5-2x^3+x^2+2=-1
The zeros of x^5-2x^3+x^2+2=-1 are x\approx-1.76436…