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

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

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

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

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

x = 0, x = - 1 + i, x = - 1 - i

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

The solutions are

x = 0, x = - 1 + i, x = - 1 - i

x^{5} + 2 x^{4} + 2 x^{3} + 4 x^{2} + 11 x + 10 = 0

x^{3} = x^{2} + 20 x

2 x^{3} - 9 x^{2} + 10 x - 3 = 0

16 x^{3} - 4 x^{2} - 20 x + 5

r^{3} - r^{2} - r + 1 = 0

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