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

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

Find the zeros of x^3+x^2+x=-1

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

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

x = - 1, x = i, x = - i

Solution steps

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

Move

1

to the left side

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 1 = 0 : x = - 1

Solve

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

The solutions are

x = - 1, x = i, x = - i

64 x^{3} + 216 (x - 1)^{3} = 0

x^{3} + 2 x^{2} + 6 x + 5 = 0

z^{6} - 2 z^{3} + 4 = 0

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

2 x^{3} + 9 x^{2} + 4 x = 0

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