What are the solutions to the equation x^4+9x^3+x^2+9=0 ?

The solutions to the equation x^4+9x^3+x^2+9=0 are x\approx-1.08774…,x\approx-8.87443…

Find the zeros of x^4+9x^3+x^2+9=0

The zeros of x^4+9x^3+x^2+9=0 are x\approx-1.08774…,x\approx-8.87443…

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x^{4} + 9 x^{3} + x^{2} + 9 = 0

x \approx - 1.08774 \dots, x \approx - 8.87443 \dots

Solution steps

x^{4} + 9 x^{3} + x^{2} + 9 = 0

Find one solution for

x^{4} + 9 x^{3} + x^{2} + 9 = 0

using Newton-Raphson:

x \approx - 1.08774 \dots

Apply long division:

\frac{x ^{4} + 9 x ^{3} + x ^{2} + 9}{x + 1.08774 \dots} = x^{3} + 7.91225 \dots x^{2} - 7.60653 \dots x + 8.27398 \dots

x^{3} + 7.91225 \dots x^{2} - 7.60653 \dots x + 8.27398 \dots \approx 0

Find one solution for

x^{3} + 7.91225 \dots x^{2} - 7.60653 \dots x + 8.27398 \dots = 0

using Newton-Raphson:

x \approx - 8.87443 \dots

Apply long division:

\frac{x ^{3} + 7.91225 \dots x ^{2} - 7.60653 \dots x + 8.27398 \dots}{x + 8.87443 \dots} = x^{2} - 0.96218 \dots x + 0.93233 \dots

x^{2} - 0.96218 \dots x + 0.93233 \dots \approx 0

Find one solution for

x^{2} - 0.96218 \dots x + 0.93233 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 1.08774 \dots, x \approx - 8.87443 \dots

x^{3} - 7 x + 10 = 0

\frac{1}{2} t^{2} (t^{2} - 2 t + 1) = 0

x^{3} - 7 x^{2} - 57 x + 15 = 0

s, s^{3} + 12 s^{2} + 20 s = 0

x^{2} - 3 = \frac{x ( x ^{2} - 9 )}{4}

What are the solutions to the equation x^4+9x^3+x^2+9=0 ?
The solutions to the equation x^4+9x^3+x^2+9=0 are x\approx-1.08774…,x\approx-8.87443…
Find the zeros of x^4+9x^3+x^2+9=0
The zeros of x^4+9x^3+x^2+9=0 are x\approx-1.08774…,x\approx-8.87443…