Let $$\alpha $$ and $$\beta $$ be the roots of the equation 5x2 + 6x – 2 = 0. If Sn = $$\alpha $$n + $$\beta $$n, n = 1, 2, 3...., then :
JEE · Math · previous-year question
- A.5S6 + 6S5 = 2S4correct
- B.5S6 + 6S5 + 2S4 = 0
- C.6S6 + 5S5 + 2S4 = 0
- D.6S6 + 5S5 = 2S4
Answer
A. 5S6 + 6S5 = 2S4
Explanation
$$\alpha $$ and $$\beta $$ be the roots of the equation 5x2 + 6x – 2 = 0. $$ \Rightarrow $$ 5$$\alpha $$2 + 6$$\alpha $$ - 2 = 0 $$ \Rightarrow $$ 5$$\alpha $$n + 2 + 6$$\alpha $$n + 2 - 2$$\alpha $$n = 0 ......(1) (By multiplying $$\alpha $$n) Similarly 5$$\beta $$n + 2 + 6$$\beta $$n + 2 - 2$$\beta $$n = 0 ......(2) By adding (1) & (2) 5Sn+2 + 6Sn+1 – 2Sn = 0 For n = 4 5S6 + 6S5 = 2S4
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