Question

identify all real roots of x^3-9x^2+16x-8=0

Answer 1

let f(x) = x^3-9x^2+16x-8
try x = ±1, ±2, ±4, ±8 , hoping to get f(x) = 0

wow, after one try ...
f(1) = 1 - 9 + 16 - 8 = 0
so x-1 is a factor
using synthetic division I had the other factor as
x^2 - 8x + 8

so x^2 - 8x + 8 = 0
I will use completing the square , since the middle term is even

x^2 - 8x + 16 = -8 + 16
(x-4)^2 = 8
x-4 = ±√8 = ± 2√2

x = 4 ± 2√2 or x = 1