Calculate a polynomial function g with integer coefficient that has ∛28 as a root, and then use the Newton-Raphson method with c₀ =3 to calculate c₁?

Given root of polynomial function x=∛28

g(2)=x³ -28=0

Applying Newton's method

x_(n+1) = x_n - (g(x_n)) / (g'(x_n))

For c₁ ⇒ c₁ = c₀ - (g(c₀)) / (g'(c₀))

Thus, c₀ =3

So, g'(3)=27

g(3)=27-28=-1

c₁ = (3-(-1)) / (27) = (81+1) / (27)

c₁ = (82)/(27)