What are the solutions to the equation x^4+7x^3-2x^2+7x+1=0 ?

The solutions to the equation x^4+7x^3-2x^2+7x+1=0 are x\approx-0.13520…,x\approx-7.39591…

Find the zeros of x^4+7x^3-2x^2+7x+1=0

The zeros of x^4+7x^3-2x^2+7x+1=0 are x\approx-0.13520…,x\approx-7.39591…

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x^{4} + 7 x^{3} - 2 x^{2} + 7 x + 1 = 0

x \approx - 0.13520 \dots, x \approx - 7.39591 \dots

Solution steps

x^{4} + 7 x^{3} - 2 x^{2} + 7 x + 1 = 0

Find one solution for

x^{4} + 7 x^{3} - 2 x^{2} + 7 x + 1 = 0

using Newton-Raphson:

x \approx - 0.13520 \dots

Apply long division:

\frac{x ^{4} + 7 x ^{3} - 2 x ^{2} + 7 x + 1}{x + 0.13520 \dots} = x^{3} + 6.86479 \dots x^{2} - 2.92818 \dots x + 7.39591 \dots

x^{3} + 6.86479 \dots x^{2} - 2.92818 \dots x + 7.39591 \dots \approx 0

Find one solution for

x^{3} + 6.86479 \dots x^{2} - 2.92818 \dots x + 7.39591 \dots = 0

using Newton-Raphson:

x \approx - 7.39591 \dots

Apply long division:

\frac{x ^{3} + 6.86479 \dots x ^{2} - 2.92818 \dots x + 7.39591 \dots}{x + 7.39591 \dots} = x^{2} - 0.53112 \dots x + 1

x^{2} - 0.53112 \dots x + 1 \approx 0

Find one solution for

x^{2} - 0.53112 \dots x + 1 = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 0.13520 \dots, x \approx - 7.39591 \dots

x^{4} = 3 x

x^{4} = 7 x

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

x^{4} = - 3

x^{4} = - 7

What are the solutions to the equation x^4+7x^3-2x^2+7x+1=0 ?
The solutions to the equation x^4+7x^3-2x^2+7x+1=0 are x\approx-0.13520…,x\approx-7.39591…
Find the zeros of x^4+7x^3-2x^2+7x+1=0
The zeros of x^4+7x^3-2x^2+7x+1=0 are x\approx-0.13520…,x\approx-7.39591…