What are the solutions to the equation n^4+2n^3+n^2+20n=400 ?

The solutions to the equation n^4+2n^3+n^2+20n=400 are n\approx 3.77371…,n\approx-5.26760…

Find the zeros of n^4+2n^3+n^2+20n=400

The zeros of n^4+2n^3+n^2+20n=400 are n\approx 3.77371…,n\approx-5.26760…

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n^{4} + 2 n^{3} + n^{2} + 20 n = 400

n \approx 3.77371 \dots, n \approx - 5.26760 \dots

Solution steps

n^{4} + 2 n^{3} + n^{2} + 20 n = 400

Move

400

to the left side

n^{4} + 2 n^{3} + n^{2} + 20 n - 400 = 0

Find one solution for

n^{4} + 2 n^{3} + n^{2} + 20 n - 400 = 0

using Newton-Raphson:

n \approx 3.77371 \dots

Apply long division:

\frac{n ^{4} + 2 n ^{3} + n ^{2} + 20 n - 400}{n - 3.77371 \dots} = n^{3} + 5.77371 \dots n^{2} + 22.78830 \dots n + 105.99647 \dots

n^{3} + 5.77371 \dots n^{2} + 22.78830 \dots n + 105.99647 \dots \approx 0

Find one solution for

n^{3} + 5.77371 \dots n^{2} + 22.78830 \dots n + 105.99647 \dots = 0

using Newton-Raphson:

n \approx - 5.26760 \dots

Apply long division:

\frac{n ^{3} + 5.77371 \dots n ^{2} + 22.78830 \dots n + 105.99647 \dots}{n + 5.26760 \dots} = n^{2} + 0.50610 \dots n + 20.12233 \dots

n^{2} + 0.50610 \dots n + 20.12233 \dots \approx 0

Find one solution for

n^{2} + 0.50610 \dots n + 20.12233 \dots = 0

using Newton-Raphson:

No Solution for

n \in R

The solutions are

n \approx 3.77371 \dots, n \approx - 5.26760 \dots

z^{4} - 4 i = 0

3 x^{4} - 6 x^{2} - 72 = 0

b^{3} - 16 b = 0

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

2 = x^{4}

What are the solutions to the equation n^4+2n^3+n^2+20n=400 ?
The solutions to the equation n^4+2n^3+n^2+20n=400 are n\approx 3.77371…,n\approx-5.26760…
Find the zeros of n^4+2n^3+n^2+20n=400
The zeros of n^4+2n^3+n^2+20n=400 are n\approx 3.77371…,n\approx-5.26760…