What are the solutions to the equation x^4+20x^3+121x^2+490x+630=0 ?

The solutions to the equation x^4+20x^3+121x^2+490x+630=0 are x\approx-1.95352…,x\approx-13.45507…

Find the zeros of x^4+20x^3+121x^2+490x+630=0

The zeros of x^4+20x^3+121x^2+490x+630=0 are x\approx-1.95352…,x\approx-13.45507…

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x^{4} + 20 x^{3} + 121 x^{2} + 490 x + 630 = 0

x \approx - 1.95352 \dots, x \approx - 13.45507 \dots

Solution steps

x^{4} + 20 x^{3} + 121 x^{2} + 490 x + 630 = 0

Find one solution for

x^{4} + 20 x^{3} + 121 x^{2} + 490 x + 630 = 0

using Newton-Raphson:

x \approx - 1.95352 \dots

Apply long division:

\frac{x ^{4} + 20 x ^{3} + 121 x ^{2} + 490 x + 630}{x + 1.95352 \dots} = x^{3} + 18.04647 \dots x^{2} + 85.74569 \dots x + 322.49329 \dots

x^{3} + 18.04647 \dots x^{2} + 85.74569 \dots x + 322.49329 \dots \approx 0

Find one solution for

x^{3} + 18.04647 \dots x^{2} + 85.74569 \dots x + 322.49329 \dots = 0

using Newton-Raphson:

x \approx - 13.45507 \dots

Apply long division:

\frac{x ^{3} + 18.04647 \dots x ^{2} + 85.74569 \dots x + 322.49329 \dots}{x + 13.45507 \dots} = x^{2} + 4.59139 \dots x + 23.96814 \dots

x^{2} + 4.59139 \dots x + 23.96814 \dots \approx 0

Find one solution for

x^{2} + 4.59139 \dots x + 23.96814 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 1.95352 \dots, x \approx - 13.45507 \dots

x (x - 4)^{2} - 11 = 5

x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x = 0

x^{3} - 6 x^{2} + 11 x + 6 = 0

x^{3} = 27 x^{10}

x^{3} x + 1 x = \frac{2}{3}

What are the solutions to the equation x^4+20x^3+121x^2+490x+630=0 ?
The solutions to the equation x^4+20x^3+121x^2+490x+630=0 are x\approx-1.95352…,x\approx-13.45507…
Find the zeros of x^4+20x^3+121x^2+490x+630=0
The zeros of x^4+20x^3+121x^2+490x+630=0 are x\approx-1.95352…,x\approx-13.45507…