您給的 \( (x^2-x+1)(x-2)(x-\frac12)^2 = 0 \) 是三實二虛沒錯，但是不符合題意的要求: \( f(\alpha) = 0 \Rightarrow f(1-\alpha) = f(\frac1\alpha) = 0 \)

Abel's Theorem (一般在高微裡會學到)

述敘證明請見 http://www.proofwiki.org/wiki/Abel's_Theorem