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Let a,b, and c be three real numbers sat...

Let a,b, and c be three real numbers satistying `[a,b,c][(1,9,7),(8,2,7),(7,3,7)]=[0,0,0]`Let b=6, with a and c satisfying (E). If `alpha` and `beta` are the roots of the quadratic equation `ax^2+bx+c=0 then sum_(n=0)^oo (1/alpha+1/beta)^n` is (A) 6 (B) 7 (C) `6/7` (D) oo

A

6

B

7

C

`6/7`

D

`oo`

Text Solution

Verified by Experts

The correct Answer is:
B
`ax^(2)+bx+c=0`
`implies x^(2)+6x-7=0`
`implies alpha=1, beta=-7`
`sum_(n=0)^(oo) (1/alpha+1/beta)^(n)= sum_(n=0)^(oo) (1/1-1/7)^(n)`
`=sum_(n=0)^(oo) (6/7)^(n)`
`=1/(1-6/7)=7`
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