What are the solutions to the equation y^4+3y^3-2y^2-y+1=0 ?

The solutions to the equation y^4+3y^3-2y^2-y+1=0 are y\approx-0.68552…,y\approx-3.46943…

Find the zeros of y^4+3y^3-2y^2-y+1=0

The zeros of y^4+3y^3-2y^2-y+1=0 are y\approx-0.68552…,y\approx-3.46943…

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y^{4} + 3 y^{3} - 2 y^{2} - y + 1 = 0

y \approx - 0.68552 \dots, y \approx - 3.46943 \dots

Solution steps

y^{4} + 3 y^{3} - 2 y^{2} - y + 1 = 0

Find one solution for

y^{4} + 3 y^{3} - 2 y^{2} - y + 1 = 0

using Newton-Raphson:

y \approx - 0.68552 \dots

Apply long division:

\frac{y ^{4} + 3 y ^{3} - 2 y ^{2} - y + 1}{y + 0.68552 \dots} = y^{3} + 2.31447 \dots y^{2} - 3.58663 \dots y + 1.45873 \dots

y^{3} + 2.31447 \dots y^{2} - 3.58663 \dots y + 1.45873 \dots \approx 0

Find one solution for

y^{3} + 2.31447 \dots y^{2} - 3.58663 \dots y + 1.45873 \dots = 0

using Newton-Raphson:

y \approx - 3.46943 \dots

Apply long division:

\frac{y ^{3} + 2.31447 \dots y ^{2} - 3.58663 \dots y + 1.45873 \dots}{y + 3.46943 \dots} = y^{2} - 1.15496 \dots y + 0.42045 \dots

y^{2} - 1.15496 \dots y + 0.42045 \dots \approx 0

Find one solution for

y^{2} - 1.15496 \dots y + 0.42045 \dots = 0

using Newton-Raphson:

No Solution for

y \in R

The solutions are

y \approx - 0.68552 \dots, y \approx - 3.46943 \dots

x^{3} = \frac{27}{8}

8 x^{3} - 3 x^{2} - 3 x - 1 = 0

- 3 x (x + 9) (x^{2} + 1) = 0

16 z^{4} - 4 z^{2} + 1 = 0

5 x^{3} - 27 x^{2} - 17 x - 6 = 0

What are the solutions to the equation y^4+3y^3-2y^2-y+1=0 ?
The solutions to the equation y^4+3y^3-2y^2-y+1=0 are y\approx-0.68552…,y\approx-3.46943…
Find the zeros of y^4+3y^3-2y^2-y+1=0
The zeros of y^4+3y^3-2y^2-y+1=0 are y\approx-0.68552…,y\approx-3.46943…