jee-main 2020 Q51

jee-main · India · session2_02sep_shift1 Roots of polynomials Vieta's formulas: compute symmetric functions of roots

Let $\alpha$ and $\beta$ be the roots of the equation, $5x^{2} + 6x - 2 = 0$. If $S_{n} = \alpha^{n} + \beta^{n}, n = 1,2,3,\ldots$, then
(1) $6S_{6} + 5S_{5} = 2S_{4}$
(2) $5S_{6} + 6S_{5} + 2S_{4} = 0$
(3) $5S_{6} + 6S_{5} = 2S_{4}$
(4) $6S_{6} + 5S_{5} + 2S_{4} = 0$

Let $\alpha$ and $\beta$ be the roots of the equation, $5x^{2} + 6x - 2 = 0$. If $S_{n} = \alpha^{n} + \beta^{n}, n = 1,2,3,\ldots$, then\\
(1) $6S_{6} + 5S_{5} = 2S_{4}$\\
(2) $5S_{6} + 6S_{5} + 2S_{4} = 0$\\
(3) $5S_{6} + 6S_{5} = 2S_{4}$\\
(4) $6S_{6} + 5S_{5} + 2S_{4} = 0$

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