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

  • [JEE MAIN 2020]
  • A

    $5 \mathrm{S}_{6}+6 \mathrm{S}_{5}=2 \mathrm{S}_{4}$

  • B

    $5 \mathrm{S}_{6}+6 \mathrm{S}_{5}+2 \mathrm{S}_{4}=0$

  • C

    $6 \mathrm{S}_{6}+5 \mathrm{S}_{5}+2 \mathrm{S}_{4}=0$

  • D

    $6 \mathrm{S}_{6}+5 \mathrm{S}_{5}=2 \mathrm{S}_{4}$

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