For Any Field F Let Fx Xn An1xnl

For any field F, let f(x) = xn + an-1xn-l + ∙∙∙∙∙∙∙∙ + a1x + a0 ∈ F[x]. lf r1,r2, . . ., rn are the roots of f(x), and r1 ∈ F for all 1 (a) -an-i – r1 + r2 + • • • + rn.
b) (-1 )na0 = r1xr2 ∙∙∙∙∙∙ – rn.

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