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這是複變函數的一個簡單結論,可以採用劉維爾定理:有界整函數必為常數.若n次多項式(多項式是整函數)無根,則其倒數在擴充複平面解析(無窮遠點是可去奇點),從而利用劉維爾定理,有其倒數是常數(因為其倒數是有界的).從而本身是常數.這與其實多項式衝突.得證 另外說一句,如果想用代數方法證明將是非常困難的.
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