What are the solutions to the equation z^3-z+6=0 ?

The solutions to the equation z^3-z+6=0 are z=-2,z=1+sqrt(2)i,z=1-sqrt(2)i

Find the zeros of z^3-z+6=0

The zeros of z^3-z+6=0 are z=-2,z=1+sqrt(2)i,z=1-sqrt(2)i

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z^{3} - z + 6 = 0

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

Solution steps

z^{3} - z + 6 = 0

Factor

z^{3} - z + 6 : (z + 2) (z^{2} - 2 z + 3)

(z + 2) (z^{2} - 2 z + 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

z + 2 = 0 : z = - 2

Solve

z^{2} - 2 z + 3 = 0 : z = 1 + 2 i, z = 1 - 2 i

The solutions are

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

2 x^{3} - 3 x^{2} - 10 x + 15 = 0

x = - x^{3}

0 = x^{3} - 7 x^{2} - x + 7

x^{3} + 2 x^{2} - 40 x + 64 = 0

x^{3} + 3 x^{2} - 4 x - 12 = 0

What are the solutions to the equation z^3-z+6=0 ?
The solutions to the equation z^3-z+6=0 are z=-2,z=1+sqrt(2)i,z=1-sqrt(2)i
Find the zeros of z^3-z+6=0
The zeros of z^3-z+6=0 are z=-2,z=1+sqrt(2)i,z=1-sqrt(2)i