Let a and b be the roots of the equation, 2 5 6 2 0. x x + -= If , 1, 2,3, …, n n n S n =a +b = then :

Question:

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 :

  1. $6 S_{6}+5 S_{5}=2 S_{4}$

  2. $6 S_{6}+5 S_{5}+2 S_{4}=0$

  3. $5 S_{6}+6 S_{5}=2 S_{4}$

  4. $5 S_{6}+6 S_{5}+2 S_{4}=0$

Correct Option: 3

JEE Main Previous Year 1 Question of JEE Main from Mathematics Complex Numbers and Quadratic Equations chapter.
JEE Main Previous Year Sep. 02, 2020 (I)

Solution:

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