What are the solutions to the equation 8x^4-96x^3+320x^2+588x-1764=0 ?

The solutions to the equation 8x^4-96x^3+320x^2+588x-1764=0 are x\approx 1.94668…,x\approx-2.31127…

Find the zeros of 8x^4-96x^3+320x^2+588x-1764=0

The zeros of 8x^4-96x^3+320x^2+588x-1764=0 are x\approx 1.94668…,x\approx-2.31127…

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8 x^{4} - 96 x^{3} + 320 x^{2} + 588 x - 1764 = 0

x \approx 1.94668 \dots, x \approx - 2.31127 \dots

Solution steps

8 x^{4} - 96 x^{3} + 320 x^{2} + 588 x - 1764 = 0

Find one solution for

8 x^{4} - 96 x^{3} + 320 x^{2} + 588 x - 1764 = 0

using Newton-Raphson:

x \approx 1.94668 \dots

Apply long division:

\frac{8 x ^{4} - 96 x ^{3} + 320 x ^{2} + 588 x - 1764}{x - 1.94668 \dots} = 8 x^{3} - 80.42652 \dots x^{2} + 163.43495 \dots x + 906.15623 \dots

8 x^{3} - 80.42652 \dots x^{2} + 163.43495 \dots x + 906.15623 \dots \approx 0

Find one solution for

8 x^{3} - 80.42652 \dots x^{2} + 163.43495 \dots x + 906.15623 \dots = 0

using Newton-Raphson:

x \approx - 2.31127 \dots

Apply long division:

\frac{8 x ^{3} - 80.42652 \dots x ^{2} + 163.43495 \dots x + 906.15623 \dots}{x + 2.31127 \dots} = 8 x^{2} - 98.91673 \dots x + 392.05884 \dots

8 x^{2} - 98.91673 \dots x + 392.05884 \dots \approx 0

Find one solution for

8 x^{2} - 98.91673 \dots x + 392.05884 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1.94668 \dots, x \approx - 2.31127 \dots

m^{4} = 625

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

x^{5} - 16 x = 0

x^{3} = - 27

x^{3} + x = 16

What are the solutions to the equation 8x^4-96x^3+320x^2+588x-1764=0 ?
The solutions to the equation 8x^4-96x^3+320x^2+588x-1764=0 are x\approx 1.94668…,x\approx-2.31127…
Find the zeros of 8x^4-96x^3+320x^2+588x-1764=0
The zeros of 8x^4-96x^3+320x^2+588x-1764=0 are x\approx 1.94668…,x\approx-2.31127…