Let `r` be a root of the equation `x^2+2x+6=0`. The value of `(r+2)(r+3)(r+4)(r+5)` is

Let alpha, beta be the roots of the equation x^(2) - px + r = 0 and (alpha)/(2) , 2 beta be the roots of the equation x^(2) - qx + r = 0 . Then the value of r is :

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

Let alpha,beta be the roots of the equation x^2-p x+r=0a n dalpha//2,2beta be the roots of the equation x^2-q x+r=0. Then the value of r is

Let alpha,beta be the equation x^2-px+r=0 and alpha/2,2beta be the roots of the equation x^2-qx+r=0. Then, the value of r is

Let alpha,beta be the roots of the equation x^2-p x+r=0 and alpha/2,2beta be the roots of the equation x^2-q x+r=0 , the value of r 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 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 :