Verified Solution • 2025–26 Session moderate

QJEEM20Ma33ee: JEE Main 2020 Mathematics - Class 11 JEEM20Ma33ee Solution: Let and be the roots of the equation 5x 2 + 6x – 2 = 0. If S n…

Let α\alpha and β\beta be the roots of the equation
5x2 + 6x – 2 = 0. If Sn = α\alpha n + β\beta n, n = 1, 2, 3...., then :

Multiple Choice Options

  • A 5S6 + 6S5 = 2S4
  • B 5S6 + 6S5 + 2S4 = 0
  • C 6S6 + 5S5 + 2S4 = 0
  • D 6S6 + 5S5 = 2S4

Step-by-Step Verified Solution

α\alpha and β\beta be the roots of the equation
5x2 + 6x – 2 = 0.

⇒\Rightarrow 5 α\alpha 2 + 6 α\alpha - 2 = 0

⇒\Rightarrow 5 α\alpha n + 2 + 6 α\alpha n + 2 - 2 α\alpha n = 0 ......(1)

(By multiplying α\alpha n)

Similarly 5 β\beta n + 2 + 6 β\beta n + 2 - 2 β\beta n = 0 ......(2)

By adding (1) & (2)

5Sn+2 + 6Sn+1 – 2Sn = 0

For n = 4

5S6 + 6S5 = 2S4

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