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If α and β are zero of f(x)=ax 2 +bx+c. The evaluate α 4 ×β 4 Note that we have =(α+β) 4 =α 4 +β 4 + 4 C 1 α 3 β 1 + 4 C 2 α 2 β 2 + 4 C 3 α 1 β 1 3 Then, α 4 +β 4 =(α+β) 4 −4(α 3 β 1 +α 1 β 3 )−6α 2 β 2 =(α+β) 4
