What are the solutions to the equation x^4-2x^3-8x-16=0 ?

The solutions to the equation x^4-2x^3-8x-16=0 are x\approx-1.23606…,x\approx 3.23606…

Find the zeros of x^4-2x^3-8x-16=0

The zeros of x^4-2x^3-8x-16=0 are x\approx-1.23606…,x\approx 3.23606…

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x^{4} - 2 x^{3} - 8 x - 16 = 0

x \approx - 1.23606 \dots, x \approx 3.23606 \dots

Solution steps

x^{4} - 2 x^{3} - 8 x - 16 = 0

Find one solution for

x^{4} - 2 x^{3} - 8 x - 16 = 0

using Newton-Raphson:

x \approx - 1.23606 \dots

Apply long division:

\frac{x ^{4} - 2 x ^{3} - 8 x - 16}{x + 1.23606 \dots} = x^{3} - 3.23606 \dots x^{2} + 4.00000 \dots x - 12.94427 \dots

x^{3} - 3.23606 \dots x^{2} + 4.00000 \dots x - 12.94427 \dots \approx 0

Find one solution for

x^{3} - 3.23606 \dots x^{2} + 4.00000 \dots x - 12.94427 \dots = 0

using Newton-Raphson:

x \approx 3.23606 \dots

Apply long division:

\frac{x ^{3} - 3.23606 \dots x ^{2} + 4.00000 \dots x - 12.94427 \dots}{x - 3.23606 \dots} = x^{2} + 4.00000 \dots

x^{2} + 4.00000 \dots \approx 0

Find one solution for

x^{2} + 4.00000 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 1.23606 \dots, x \approx 3.23606 \dots

0.12 = x^{4} - 1

x, x^{4} + 7 x^{2} - 16 = 0

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

8 x^{7} - 7 x^{8} = 0.75

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

What are the solutions to the equation x^4-2x^3-8x-16=0 ?
The solutions to the equation x^4-2x^3-8x-16=0 are x\approx-1.23606…,x\approx 3.23606…
Find the zeros of x^4-2x^3-8x-16=0
The zeros of x^4-2x^3-8x-16=0 are x\approx-1.23606…,x\approx 3.23606…