What are the solutions to the equation x^1+x^2+x^3+x^4=40 ?

The solutions to the equation x^1+x^2+x^3+x^4=40 are x\approx 2.18199…,x\approx-2.73122…

Find the zeros of x^1+x^2+x^3+x^4=40

The zeros of x^1+x^2+x^3+x^4=40 are x\approx 2.18199…,x\approx-2.73122…

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x^{1} + x^{2} + x^{3} + x^{4} = 40

x \approx 2.18199 \dots, x \approx - 2.73122 \dots

Solution steps

x^{1} + x^{2} + x^{3} + x^{4} = 40

Refine

x + x^{2} + x^{3} + x^{4} = 40

Move

40

to the left side

x + x^{2} + x^{3} + x^{4} - 40 = 0

Write in the standard form

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

x^{4} + x^{3} + x^{2} + x - 40 = 0

Find one solution for

x^{4} + x^{3} + x^{2} + x - 40 = 0

using Newton-Raphson:

x \approx 2.18199 \dots

Apply long division:

\frac{x ^{4} + x ^{3} + x ^{2} + x - 40}{x - 2.18199 \dots} = x^{3} + 3.18199 \dots x^{2} + 7.94310 \dots x + 18.33183 \dots

x^{3} + 3.18199 \dots x^{2} + 7.94310 \dots x + 18.33183 \dots \approx 0

Find one solution for

x^{3} + 3.18199 \dots x^{2} + 7.94310 \dots x + 18.33183 \dots = 0

using Newton-Raphson:

x \approx - 2.73122 \dots

Apply long division:

\frac{x ^{3} + 3.18199 \dots x ^{2} + 7.94310 \dots x + 18.33183 \dots}{x + 2.73122 \dots} = x^{2} + 0.45077 \dots x + 6.71194 \dots

x^{2} + 0.45077 \dots x + 6.71194 \dots \approx 0

Find one solution for

x^{2} + 0.45077 \dots x + 6.71194 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 2.18199 \dots, x \approx - 2.73122 \dots

x^{10} x + 8 = 6 x - 4

3 x^{3} - 8 x^{2} - 19 x + 37 = 0

2 x^{5} - 32 x = 0

4 x^{3} - 12 x^{2} + 16 = 0

x^{2} (4 x - 3) (5 x - 1) = 0

What are the solutions to the equation x^1+x^2+x^3+x^4=40 ?
The solutions to the equation x^1+x^2+x^3+x^4=40 are x\approx 2.18199…,x\approx-2.73122…
Find the zeros of x^1+x^2+x^3+x^4=40
The zeros of x^1+x^2+x^3+x^4=40 are x\approx 2.18199…,x\approx-2.73122…