Home
Class 12
MATHS
If alpha, beta be the roots of ax^(2)+bx...

If `alpha, beta` be the roots of `ax^(2)+bx+c=0(a, b, c in R), (c )/(a)lt 1` and `b^(2)-4ac lt 0, f(n)= sum_(r=1)^(n)|alpha|^(r )+|beta|^(r )`, then `lim_(n to oo)f(n)` is equal to

A

`(1)/(sqrt((a)/(c ))-1)`

B

`(1)/(sqrt((a)/(c ))-1)`

C

`(sqrt(c ))/(-sqrt(a)+sqrt(c ))`

D

`(2)/(sqrt((a)/(c ))-1)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Similar Questions

Explore conceptually related problems

If alpha , beta are the roots of ax^2+bx +c=0 then (1+ alpha + alpha ^2)(1+ beta + beta ^2) is

If alpha, beta are the roots of x^(2) - 3x + a = 0 , a in R and lt 1 lt beta, then find the values of a

If alpha and beta are the roots of the equation ax ^(2) + bx + c=0,a,b, c in R , alpha ne 0 then which is (are) correct:

If 0 lt alpha lt beta then lim_(n to oo) (beta^(n) + alpha^(n))^((1)/(n)) is equal to

If alpha, beta are the roots of a x^2 + bx + c = 0 and k in R then the condition so that alpha < k < beta is :

If alpha, beta be the roots of 4x^(8) - 16x + c = 0, c in R such that 1 lt alpha lt 2 and 2 lt beta lt 3 , then the number of integral values of c is

If alpha and beta are the roots of the quadratic equation 4x ^(2) + 2x -1=0 then the value of sum _(r =1) ^(oo) (a ^(r ) + beta ^(r )) is :

If alpha,beta are roots of x^2-3x+a=0 , a in R and alpha <1< beta then find the value of a.

If alpha and beta are the roots of the equation 375 x^(2) - 25x - 2 = 0 , then lim_(n rarr oo) Sigma_(r = 1)^n alpha^(r) + lim_(n rarr oo) Sigma_(r = 1)^n beta^(r) is equal to :

If alpha and beta (alpha lt beta) are the roots of the equation x^(2) + bx + c = 0 , where c lt 0 lt b , then