If alpha_1, alpha_2 and alpha_3 are the roots | vedclass

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(D) Given that $\alpha_1, \alpha_2, \alpha_3$ are the roots of $x^3+3x+2=0$.By Newton's Sums,let $S_n = \alpha_1^n + \alpha_2^n + \alpha_3^n$.The equa

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$30$

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(D) Given that $\alpha_1, \alpha_2, \alpha_3$ are the roots of $x^3+3x+2=0$.By Newton's Sums,let $S_n = \alpha_1^n + \alpha_2^n + \alpha_3^n$.The equation is $x^3 + 0x^2 + 3x + 2 = 0$.For $n=1$: $S_1 + 0 = 0 \Rightarrow S_1 = 0$.For $n=2$: $S_2 + 0(S_1) + 3(2) = 0 \Rightarrow S_2 = -6$.For $n=3$: $S_3 + 0(S_2) + 3(S_1) + 2(3) = 0 \Rightarrow S_3 = -6$.For $n=4$: $S_4 + 0(S_3) + 3(S_2) + 2(S_1) = 0$ $\Rightarrow S_4 + 3(-6) + 2(0) = 0$ $\Rightarrow S_4 = 18$.For $n=5$: $S_5 + 0(S_4) + 3(S_3) + 2(S_2) = 0 \Rightarrow S_5 + 3(-6) + 2(-6) = 0$.$S_5 - 18 - 12 = 0 \Rightarrow S_5 = 30$.

If $\alpha_1, \alpha_2$ and $\alpha_3$ are the roots of $x^3+3x+2=0$,then $\alpha_1^5+\alpha_2^5+\alpha_3^5=$

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