Question

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`

Answer 1

Correct Answer - 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`