What are the solutions to the equation -x^3+x^2-x+1=0 ?

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

Find the zeros of -x^3+x^2-x+1=0

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

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

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

Solution steps

- 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

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

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}

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