What are the solutions to the equation 3x^3+4x^2+4x+1=0 ?

The solutions to the equation 3x^3+4x^2+4x+1=0 are x=-1/3 ,x=-1/2+i(sqrt(3))/2 ,x=-1/2-i(sqrt(3))/2

Find the zeros of 3x^3+4x^2+4x+1=0

The zeros of 3x^3+4x^2+4x+1=0 are x=-1/3 ,x=-1/2+i(sqrt(3))/2 ,x=-1/2-i(sqrt(3))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

x = - \frac{1}{3}, x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

Solution steps

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

Factor

3 x^{3} + 4 x^{2} + 4 x + 1 : (3 x + 1) (x^{2} + x + 1)

(3 x + 1) (x^{2} + x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

3 x + 1 = 0 : x = - \frac{1}{3}

Solve

x^{2} + x + 1 = 0 : x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

The solutions are

x = - \frac{1}{3}, x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

x^{4} = 27 x

7 x^{4} = 56 x

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

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

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

What are the solutions to the equation 3x^3+4x^2+4x+1=0 ?
The solutions to the equation 3x^3+4x^2+4x+1=0 are x=-1/3 ,x=-1/2+i(sqrt(3))/2 ,x=-1/2-i(sqrt(3))/2
Find the zeros of 3x^3+4x^2+4x+1=0
The zeros of 3x^3+4x^2+4x+1=0 are x=-1/3 ,x=-1/2+i(sqrt(3))/2 ,x=-1/2-i(sqrt(3))/2