What are the solutions to the equation x^4-x^3-1=0 ?

The solutions to the equation x^4-x^3-1=0 are x\approx 1.38027…,x\approx-0.81917…

Find the zeros of x^4-x^3-1=0

The zeros of x^4-x^3-1=0 are x\approx 1.38027…,x\approx-0.81917…

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x^{4} - x^{3} - 1 = 0

x \approx 1.38027 \dots, x \approx - 0.81917 \dots

Solution steps

x^{4} - x^{3} - 1 = 0

Find one solution for

x^{4} - x^{3} - 1 = 0

using Newton-Raphson:

x \approx 1.38027 \dots

Apply long division:

\frac{x ^{4} - x ^{3} - 1}{x - 1.38027 \dots} = x^{3} + 0.38027 \dots x^{2} + 0.52488 \dots x + 0.72449 \dots

x^{3} + 0.38027 \dots x^{2} + 0.52488 \dots x + 0.72449 \dots \approx 0

Find one solution for

x^{3} + 0.38027 \dots x^{2} + 0.52488 \dots x + 0.72449 \dots = 0

using Newton-Raphson:

x \approx - 0.81917 \dots

Apply long division:

\frac{x ^{3} + 0.38027 \dots x ^{2} + 0.52488 \dots x + 0.72449 \dots}{x + 0.81917 \dots} = x^{2} - 0.43889 \dots x + 0.88441 \dots

x^{2} - 0.43889 \dots x + 0.88441 \dots \approx 0

Find one solution for

x^{2} - 0.43889 \dots x + 0.88441 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1.38027 \dots, x \approx - 0.81917 \dots

m^{3} = \frac{8}{27}

3 x^{4} - 3 x = 0

25 x^{4} + 4 = 29 x^{2}

8 x^{3} + 3 x^{2} - 16 x - 1 = 0

x = x^{5}

What are the solutions to the equation x^4-x^3-1=0 ?
The solutions to the equation x^4-x^3-1=0 are x\approx 1.38027…,x\approx-0.81917…
Find the zeros of x^4-x^3-1=0
The zeros of x^4-x^3-1=0 are x\approx 1.38027…,x\approx-0.81917…