Solve for x

Aug 2008
220
1
\(\displaystyle
x^3 - 2x^2 + 1 =0
\)

I've tried using the quadratic formula but the only solution I am getting for x is 1. It is supposed to have solutions of approximately x=-0.62 and x=1.62 also, but where do you get these answers.

Anyway, if anyone could show complete working out to see how I didn't get these solutions it will be appreciated!
 
Aug 2006
22,432
8,611
Well it is not a quadratic.
Note that \(\displaystyle x=1\) is a root so \(\displaystyle (x-1)\) is a factor.
 
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Aug 2008
220
1
Oh, yeah that's the factor theorem, right?
So, you use the factor theorem to solve for cubic and higher degree equations?