If roots of the equation `(x-1) (x-2)-k = 0 (k!=0)` be `alphq` and `beta` , and `gamma` and `delta` be the roots of the equation `(x-alpha) (x-beta) + k = 0`, then

alpha and beta are the roots of the equation x^(2)-3x+a=0 and gamma and delta are the roots of the equation x^(2)-12x+b=0 .If alpha,beta,gamma, and delta form an increasing GP., then (a,b)-

If alpha,beta,gamma,delta are the roots of the equation 9x^(4)+Kx^(2)-7x+4=0 and sum gamma delta=2 then K=

Let alpha,beta be the roots of the equation x^(2)-(2a+1)x+a=0 and gamma,delta be the roots of the equation x^(2)+(a-4)x+a-1=0. If (alpha)/(gamma)-(delta)/(beta)=(alpha delta(alpha-gamma+beta-delta))/(a) then the value of (a-1)^(-2) is

Given that alpha , gamma are roots of the equation Ax^(2)-4x+1=0 and beta , delta are roots of the equation Bx^(2)-6x+1=0 . If alpha , beta , gamma and delta are in H.P. , then

Given that alpha , gamma are roots of the equation Ax^(2)-4x+1=0 and beta , delta are roots of the equation Bx^(2)-6x+1=0 . If alpha , beta , gamma and delta are in H.P. , then

Given that alpha , gamma are roots of the equation Ax^(2)-4x+1=0 and beta , delta are roots of the equation Bx^(2)-6x+1=0 . If alpha , beta , gamma and delta are in H.P. , then

alpha,beta are the roots of the equation x^(2)-4x+lambda=0, and gamma,delta are the roots of the equation x^(2)-64x+mu=0. If alpha,beta,gamma,delta form an increasing G.P,find the values of alpha,beta,gamma,delta

If alpha,beta are the roots of the equation x^2-2x+4=0 , find alpha^(n)+beta^(n) for (a) n=3k, k in N

If alpha, beta are the roots of the equationn x^(2)-3x+5=0 and gamma, delta are the roots of the equation x^(2)+5x-3=0 , then the equation whose roots are alpha gamma+beta delta and alpha delta+beta gamma is