What are the solutions to the equation 4x^3-12x+1=0 ?

The solutions to the equation 4x^3-12x+1=0 are x\approx 0.08352…,x\approx 1.68877…,x\approx-1.77230…

Find the zeros of 4x^3-12x+1=0

The zeros of 4x^3-12x+1=0 are x\approx 0.08352…,x\approx 1.68877…,x\approx-1.77230…

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4 x^{3} - 12 x + 1 = 0

x \approx 0.08352 \dots, x \approx 1.68877 \dots, x \approx - 1.77230 \dots

Solution steps

4 x^{3} - 12 x + 1 = 0

Find one solution for

4 x^{3} - 12 x + 1 = 0

using Newton-Raphson:

x \approx 0.08352 \dots

Apply long division:

\frac{4 x ^{3} - 12 x + 1}{x - 0.08352 \dots} = 4 x^{2} + 0.33411 \dots x - 11.97209 \dots

4 x^{2} + 0.33411 \dots x - 11.97209 \dots \approx 0

Find one solution for

4 x^{2} + 0.33411 \dots x - 11.97209 \dots = 0

using Newton-Raphson:

x \approx 1.68877 \dots

Apply long division:

\frac{4 x ^{2} + 0.33411 \dots x - 11.97209 \dots}{x - 1.68877 \dots} = 4 x + 7.08921 \dots

4 x + 7.08921 \dots \approx 0

x \approx - 1.77230 \dots

The solutions are

x \approx 0.08352 \dots, x \approx 1.68877 \dots, x \approx - 1.77230 \dots

x^{4} + 7 x^{2} + 12 = 0

5000 \cdot x^{10} = 8000

0 = x^{4} - 9 x^{2}

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

64 x^{3} - 125 = 0

What are the solutions to the equation 4x^3-12x+1=0 ?
The solutions to the equation 4x^3-12x+1=0 are x\approx 0.08352…,x\approx 1.68877…,x\approx-1.77230…
Find the zeros of 4x^3-12x+1=0
The zeros of 4x^3-12x+1=0 are x\approx 0.08352…,x\approx 1.68877…,x\approx-1.77230…