What are the solutions to the equation z^3-6z-4=0 ?

The solutions to the equation z^3-6z-4=0 are z=-2,z=1+sqrt(3),z=1-sqrt(3)

Find the zeros of z^3-6z-4=0

The zeros of z^3-6z-4=0 are z=-2,z=1+sqrt(3),z=1-sqrt(3)

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

z = - 2, z = 1 + 3, z = 1 - 3

Decimal

z = - 2, z = 2.73205 \dots, z = - 0.73205 \dots

Solution steps

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

Factor

z^{3} - 6 z - 4 : (z + 2) (z^{2} - 2 z - 2)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

z + 2 = 0 : z = - 2

Solve

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

The solutions are

z = - 2, z = 1 + 3, z = 1 - 3

(10 x + 1) + (5 x^{29}) = 180

240 x - 60 x^{3} = 0

2 x^{3} - 3 x^{2} - 14 x + 21 = 0

7 x^{2} + 15 x = 2 x^{3}

x^{4} - x^{3} - 3 x^{2} + 5 x - 2 = 0

What are the solutions to the equation z^3-6z-4=0 ?
The solutions to the equation z^3-6z-4=0 are z=-2,z=1+sqrt(3),z=1-sqrt(3)
Find the zeros of z^3-6z-4=0
The zeros of z^3-6z-4=0 are z=-2,z=1+sqrt(3),z=1-sqrt(3)