Posted by **alicia** on Thursday, March 7, 2013 at 10:17am.

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

- math -
**Reiny**, Thursday, March 7, 2013 at 10:23am
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

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