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

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

Find the zeros of m^4+m^3+m^2=0

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

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

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

Solution steps

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

Factor

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

m^{2} (m^{2} + m + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

m = 0 or m^{2} + m + 1 = 0

Solve

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

The solutions are

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

x^{3} - 3 x^{2} - 2 x + 6 = 0

(x^{2} - x)^{2} - 14 (x^{2} - x) + 24 = 0

0 = x^{4} - 25

x^{3} + 3 x^{2} - 6 x - 18 = 0

8 y^{3} - 27 = 0

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