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

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

Find the zeros of x(x^3-1)=0

The zeros of x(x^3-1)=0 are x=0,x=1,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 >

x (x^{3} - 1) = 0

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

Solution steps

x (x^{3} - 1) = 0

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

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

8 x^{3} - 50 x = 0

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

x^{3} + 9 x^{2} + 27 x + 19 = 0

x^{3} = 3 x^{2}

2 x^{3} - 24 x^{2} + 64 x = 0

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