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For a cubic poltnomial a_3x^3+a_2x^2+a_1x+a_0 the roots r_1,r_2,r_3 come in three symmetric combinations: C_1=r_1+r_2+r_3,C_2=r_1r_2+r_2r_3+r_3r_1,C_3=r_1r_2r_3 The sum of the k^(th) powers of the roots is defined as S_k=r_1^k+r_2^k+r_3^k Then a_3S_1+a_2=0 a_3S_2+a_2S_1+2a_1=0 |
Answer» only (i) is true |
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