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

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

Find the zeros of z^3-z^2+4z-4=0

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

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

z = 1, z = 2 i, z = - 2 i

Solution steps

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

Factor

z^{3} - z^{2} + 4 z - 4 : (z - 1) (z^{2} + 4)

(z - 1) (z^{2} + 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

z - 1 = 0 or z^{2} + 4 = 0

Solve

z - 1 = 0 : z = 1

Solve

z^{2} + 4 = 0 : z = 2 i, z = - 2 i

The solutions are

z = 1, z = 2 i, z = - 2 i

x^{4} - (4 \cdot x) + 5 = 0

y^{5} + y^{3} + y = 3

- 3 = x^{6} - 8

x^{2} (x^{2} - 4) = x^{4} (x^{2} - 4)

x^{4} - 5 x^{3} + 4 = 0

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