Posted by alicia on .
identify all real roots of x^39x^2+16x8=0

math 
Reiny,
let f(x) = x^39x^2+16x8
try x = ±1, ±2, ±4, ±8 , hoping to get f(x) = 0
wow, after one try ...
f(1) = 1  9 + 16  8 = 0
so x1 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
(x4)^2 = 8
x4 = ±√8 = ± 2√2
x = 4 ± 2√2 or x = 1