What are the solutions to the equation x^4-2x^3-5=0 ?

The solutions to the equation x^4-2x^3-5=0 are x\approx-1.16469…,x\approx 2.37379…

Find the zeros of x^4-2x^3-5=0

The zeros of x^4-2x^3-5=0 are x\approx-1.16469…,x\approx 2.37379…

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

x \approx - 1.16469 \dots, x \approx 2.37379 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx - 1.16469 \dots

Apply long division:

\frac{x ^{4} - 2 x ^{3} - 5}{x + 1.16469 \dots} = x^{3} - 3.16469 \dots x^{2} + 3.68590 \dots x - 4.29296 \dots

x^{3} - 3.16469 \dots x^{2} + 3.68590 \dots x - 4.29296 \dots \approx 0

Find one solution for

x^{3} - 3.16469 \dots x^{2} + 3.68590 \dots x - 4.29296 \dots = 0

using Newton-Raphson:

x \approx 2.37379 \dots

Apply long division:

\frac{x ^{3} - 3.16469 \dots x ^{2} + 3.68590 \dots x - 4.29296 \dots}{x - 2.37379 \dots} = x^{2} - 0.79089 \dots x + 1.80847 \dots

x^{2} - 0.79089 \dots x + 1.80847 \dots \approx 0

Find one solution for

x^{2} - 0.79089 \dots x + 1.80847 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 1.16469 \dots, x \approx 2.37379 \dots

3 x^{3} + 4 x^{2} + 4 x + 1 = 0

x^{4} = 27 x

7 x^{4} = 56 x

3 x^{3} - 3 x + 1 = 0

x^{4} + 3 x^{2} - 28 = 0

What are the solutions to the equation x^4-2x^3-5=0 ?
The solutions to the equation x^4-2x^3-5=0 are x\approx-1.16469…,x\approx 2.37379…
Find the zeros of x^4-2x^3-5=0
The zeros of x^4-2x^3-5=0 are x\approx-1.16469…,x\approx 2.37379…