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 equal to-

let z_1,z_2,z_3 and z_4 be the roots of the equation z^4 + z^3 +2=0 , then the value of prod_(r=1)^(4) (2z_r+1) is equal to :

let z_1,z_2,z_3 and z_4 be the roots of the equation z^4 + z^3 +2=0 , then the value of prod_(r=1)^(4) (2z_r+1) is equal to :

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 :

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 :

Let r_(1), r_(2) and r_(3) be the solutions of the equation x^(3) - 2 x^(2)+4 x+5074=0 , then the value of (r_(1) +2)(r_(2)+2)(r_(3)+2)

Let alpha,beta be the roots of 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

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 value of r is