- #1

- 2,111

- 18

[tex]

p(X)=(X-z_1)\cdots (X-z_N)

[/tex]

holds with some [itex]z_1,\ldots, z_N\in\mathbb{C}[/itex]. Now all [itex]z_1,\ldots, z_N[/itex] are distinct.

Why is this claim true?

For example, if [itex]z_1=z_2[/itex], then [itex](X-z_1)^2[/itex] divides [itex]p[/itex], but I see no reason to assume that [itex](X-z_1)^2\in\mathbb{F}[X][/itex], so the claim remains a mystery to me.