Question

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

Answer 1

Correct Answer - B
`"If" b = 6 rArr a = 1 " and " c =-7`
`therefore ax^(2) + bx +c = 0 rArr x^(2) + 6x -7=0`
`rArr (x +7) (x -1) = 0`
`therefore x = 1, -7`
`rArr overset(oo)underset(n = 0)(sum) ((1)/(1)-(1)/(7))^(n) = 1 + (6)/(7) + ((6)/(7))^(2) + …… + oo = (1)/(1-(6)/(7)) = (1)/(1//7) = 7`