" 7.If the difference of the roots of "x^(2)-lambda x+8=0" be "2" ,the value of "lambda" is "

Let alpha , beta be the roots of x^(2) + (3- lambda) x - lambda =0 , then the value of lambda for which alpha^(2) + beta^(2) is minimum, is-

If cos^(4)alpha+k and sin^(4)alpha+k are the roots of x^(2)+lambda(2x+1)=0 and sin^(2)alpha+1 and cos^(2)alpha+1 are the roots of x^(2)+8x+4=0, then the sum of the possible values of lambda is

If cos^4 alpha +k and sin^4 alpha+k are the roots of x^2+lambda(2 x+1)=0 and sin^2 alpha+1 and cos^2 alpha +1 are the roots of x^2 +8 x+4=0, then the sum of the possible values of lambda is

If cos^4 alpha +k and sin^4 alpha+k are the roots of x^2+lambda(2 x+1)=0 and sin^2 alpha+1 and cos^2 alpha +1 are the roots of x^2 +8 x+4=0, then the sum of the possible values of lambda is

If cos^4 alpha +k and sin^4 alpha+k are the roots of x^2+lambda(2 x+1)=0 and sin^2 alpha+1 and cos^2 alpha +1 are the roots of x^2 +8 x+4=0, then the sum of the possible values of lambda is

If alpha,beta are roots of x^2-x+2lambda=0 and alpha,gamma are roots of 3x^2-10x+27lambda=0 then value of (betagamma)/(lambda) is

If lambda in R is such that the sum of the cubes of the roots of the equation x^(2)+(2-lambda)x+(10-lambda)=0 is minimum then the magnitude of the difference of the roots of this equation is :

alpha,beta are roots of lambda(x^(2)-x)+x+5=0 If lambda1 and lambda2 are the two values of lambda for which the roots alpha,beta are connected by the realation (alpha)/(beta)+(beta)/(alpha)=4 then the value of (((lambda1)/(lambda2)+(lambda2)/(lambda1))/(14)) is:

If one root of the equation 3x^(2)-5x+lambda=0 is the reciprocal of the other, then the value of lambda is

If the equation x^(2)+lambda x+mu=0 has equal roots and one root of the equation x^(2)+lambda x-12=0 is 2 ,then (lambda,mu) =