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

The solutions to the equation x^4+4x^3-1=0 are x\approx 0.60123…,x\approx-4.01544…

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

The zeros of x^4+4x^3-1=0 are x\approx 0.60123…,x\approx-4.01544…

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

x \approx 0.60123 \dots, x \approx - 4.01544 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.60123 \dots

Apply long division:

\frac{x ^{4} + 4 x ^{3} - 1}{x - 0.60123 \dots} = x^{3} + 4.60123 \dots x^{2} + 2.76640 \dots x + 1.66325 \dots

x^{3} + 4.60123 \dots x^{2} + 2.76640 \dots x + 1.66325 \dots \approx 0

Find one solution for

x^{3} + 4.60123 \dots x^{2} + 2.76640 \dots x + 1.66325 \dots = 0

using Newton-Raphson:

x \approx - 4.01544 \dots

Apply long division:

\frac{x ^{3} + 4.60123 \dots x ^{2} + 2.76640 \dots x + 1.66325 \dots}{x + 4.01544 \dots} = x^{2} + 0.58578 \dots x + 0.41421 \dots

x^{2} + 0.58578 \dots x + 0.41421 \dots \approx 0

Find one solution for

x^{2} + 0.58578 \dots x + 0.41421 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.60123 \dots, x \approx - 4.01544 \dots

s^{5} + s^{4} + 4 s^{3} + 24 s^{2} + 3 s + 63 = 0

27 x^{5} - 54 x^{4} - 72 x^{3} - 26 x^{2} - 3 x = 0

x^{3} - 7 x + 2 = 0

3 x^{4} - 7 x^{3} - 9 x^{2} + 24 x - 4

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

What are the solutions to the equation x^4+4x^3-1=0 ?
The solutions to the equation x^4+4x^3-1=0 are x\approx 0.60123…,x\approx-4.01544…
Find the zeros of x^4+4x^3-1=0
The zeros of x^4+4x^3-1=0 are x\approx 0.60123…,x\approx-4.01544…