Answer:
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
