What are the solutions to the equation x^4+24x^3+122x^2-52x+25=0 ?

The solutions to the equation x^4+24x^3+122x^2-52x+25=0 are x\approx-8.10124…,x\approx-16.32680…

Find the zeros of x^4+24x^3+122x^2-52x+25=0

The zeros of x^4+24x^3+122x^2-52x+25=0 are x\approx-8.10124…,x\approx-16.32680…

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x^{4} + 24 x^{3} + 122 x^{2} - 52 x + 25 = 0

x \approx - 8.10124 \dots, x \approx - 16.32680 \dots

Solution steps

x^{4} + 24 x^{3} + 122 x^{2} - 52 x + 25 = 0

Find one solution for

x^{4} + 24 x^{3} + 122 x^{2} - 52 x + 25 = 0

using Newton-Raphson:

x \approx - 8.10124 \dots

Apply long division:

\frac{x ^{4} + 24 x ^{3} + 122 x ^{2} - 52 x + 25}{x + 8.10124 \dots} = x^{3} + 15.89875 \dots x^{2} - 6.79969 \dots x + 3.08594 \dots

x^{3} + 15.89875 \dots x^{2} - 6.79969 \dots x + 3.08594 \dots \approx 0

Find one solution for

x^{3} + 15.89875 \dots x^{2} - 6.79969 \dots x + 3.08594 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

x \approx - 16.32680 \dots

The solutions are

x \approx - 8.10124 \dots, x \approx - 16.32680 \dots

y^{7} - 2 y^{5} + y^{3} = 0

a^{3} + a^{2} = 80

x^{3} - 2 x^{2} - 9 x + 18

(2 x - 2)^{2} (x - 2) = (2 x - 2) (x - 2)^{2}

x^{5} + 8 x^{3} = 0

What are the solutions to the equation x^4+24x^3+122x^2-52x+25=0 ?
The solutions to the equation x^4+24x^3+122x^2-52x+25=0 are x\approx-8.10124…,x\approx-16.32680…
Find the zeros of x^4+24x^3+122x^2-52x+25=0
The zeros of x^4+24x^3+122x^2-52x+25=0 are x\approx-8.10124…,x\approx-16.32680…