What are the solutions to the equation w+w^2-w^3+w^4=5 ?

The solutions to the equation w+w^2-w^3+w^4=5 are w\approx 1.45767…,w\approx-1.27049…

Find the zeros of w+w^2-w^3+w^4=5

The zeros of w+w^2-w^3+w^4=5 are w\approx 1.45767…,w\approx-1.27049…

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w + w^{2} - w^{3} + w^{4} = 5

w \approx 1.45767 \dots, w \approx - 1.27049 \dots

Solution steps

w + w^{2} - w^{3} + w^{4} = 5

Move

5

to the left side

w + w^{2} - w^{3} + w^{4} - 5 = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

w^{4} - w^{3} + w^{2} + w - 5 = 0

Find one solution for

w^{4} - w^{3} + w^{2} + w - 5 = 0

using Newton-Raphson:

w \approx 1.45767 \dots

Apply long division:

\frac{w ^{4} - w ^{3} + w ^{2} + w - 5}{w - 1.45767 \dots} = w^{3} + 0.45767 \dots w^{2} + 1.66713 \dots w + 3.43013 \dots

w^{3} + 0.45767 \dots w^{2} + 1.66713 \dots w + 3.43013 \dots \approx 0

Find one solution for

w^{3} + 0.45767 \dots w^{2} + 1.66713 \dots w + 3.43013 \dots = 0

using Newton-Raphson:

w \approx - 1.27049 \dots

Apply long division:

\frac{w ^{3} + 0.45767 \dots w ^{2} + 1.66713 \dots w + 3.43013 \dots}{w + 1.27049 \dots} = w^{2} - 0.81282 \dots w + 2.69982 \dots

w^{2} - 0.81282 \dots w + 2.69982 \dots \approx 0

Find one solution for

w^{2} - 0.81282 \dots w + 2.69982 \dots = 0

using Newton-Raphson:

No Solution for

w \in R

The solutions are

w \approx 1.45767 \dots, w \approx - 1.27049 \dots

x^{3} - 6 x^{2} + 32 = 0

3 a^{3} + 9 a - 8 = 0

x, x^{3} y^{3} - 4 = 0

x^{3} - 2 x^{2} + 16 x = 0

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

What are the solutions to the equation w+w^2-w^3+w^4=5 ?
The solutions to the equation w+w^2-w^3+w^4=5 are w\approx 1.45767…,w\approx-1.27049…
Find the zeros of w+w^2-w^3+w^4=5
The zeros of w+w^2-w^3+w^4=5 are w\approx 1.45767…,w\approx-1.27049…