Problem 17.9 (30). Let a,, an EC be roots of f(X) An-1Xn- +. + ... +...

 

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Problem 17.9 (30). Let a₁,, an EC be roots of f(X) An-1Xn-¹ +. + ... + a₁X + ao € C[X] and Prove that Sk = k Sk = a₁ + = a₁ + +ah (k≥ 1) -kan-k n ... i=1 k-1 Σ an-iSk-i (1≤k ≤n) i=1 -Σan-iSk-i (n + 1 ≤k) = Xn + Problem 17.9 (30). Let a₁,, an EC be roots of f(X) An-1Xn-¹ +. + ... + a₁X + ao € C[X] and Prove that Sk = k Sk = a₁ + = a₁ + +ah (k≥ 1) -kan-k n ... i=1 k-1 Σ an-iSk-i (1≤k ≤n) i=1 -Σan-iSk-i (n + 1 ≤k) = Xn +

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Given a i is a root of the equation ai will be the other root Let the third ro... View the full answer