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

The solutions to the equation x^3+x^2+2x=0 are x=0,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2

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

The zeros of x^3+x^2+2x=0 are x=0,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2

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

x = 0, x = - \frac{1}{2} + i \frac{7}{2}, x = - \frac{1}{2} - i \frac{7}{2}

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x^{2} + x + 2 = 0 : x = - \frac{1}{2} + i \frac{7}{2}, x = - \frac{1}{2} - i \frac{7}{2}

The solutions are

x = 0, x = - \frac{1}{2} + i \frac{7}{2}, x = - \frac{1}{2} - i \frac{7}{2}

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

x^{4} = 8 x

x^{3} + 5 x^{2} - 20 = 0

18 x^{3} + 9 x^{2} - 2 x - 1 = 0

4 x^{3} - 1 = 2 x^{2} - 2 x

What are the solutions to the equation x^3+x^2+2x=0 ?
The solutions to the equation x^3+x^2+2x=0 are x=0,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2
Find the zeros of x^3+x^2+2x=0
The zeros of x^3+x^2+2x=0 are x=0,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2