Determine all the roots given function (solve for the unknown variable)?

The roots are:

a) z1 = 0

b) z2 = -2

c) z3 = ∛2 or 1.26

Step-by-step explanation:

First we factor z from the original equation

       z⁷ + 6z⁴ - 16 z = z ( z⁶ + 6z³ -16)

                                  z ((z³)² + 6z³ -16)             express z⁶ as a power

                                  z (z³ + 8)(z³ -2)                factor

   Now, equal to zero each term

    z1 = 0           first answer

    z³ + 8 = 0         z³ = -8          z2 = -2             second answer

    z³ -2 = 0           z³ = 2            z3 = ∛2 or 1.26   third answer

the answers c

answer: idk

step-by-step explanation: