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 alpha , beta are the roots of lambda(x^(2)+x)+x+5 =0 and lambda_(1) , lambda_(2) are the two values of lambda for which alpha , beta are connected by the relation (alpha)/(beta)+(beta)/(alpha) =4, then the value of (lambda_(1))/(lambda_(2))+(lambda_(2))/(lambda_(1)) =

If alpha and beta are the roots of the equation x^(2)-5 lambda x-lambda^(2)=0 and alpha^(2)+beta^(2)=27/4 ,then the value of lambda^(2) is

If alpha,beta be the roots of the equation 4x^(2)-16x+lambda=0 where lambda in R such that 1

If alpha,beta be the roots of the equation lambda^(2)(x^(2)-x)+2 lambda x+3=0 and lambda_(1),lambda_(2) be the two values of lambda for which alpha and beta are connected by the relation (alpha)/(beta)+(beta)/(alpha)=(4)/(3), then find the equation whose roots are ((lambda_(1))^(2))/(lambda_(2)) and ((lambda_(2))^(2))/(lambda_(1))

If alpha and beta are the roots of 2x^(2) + 5x - 4 = 0 then find the value of (alpha)/(beta) + (beta)/(alpha) .

alpha , beta are roots of the equation lambda(x^(2)-x)+x+5=0. If lambda_1 and lambda_2 are the two values of lambda for which the roots alpha , beta are connected b the relation (alpha )/(beta)+(beta)/(alpha)=4 , then the value of (lambda_1)/(lambda_2)+(lambda_2)/(lambda_1) is :

If alpha and beta are the roots of the equation x^(2)+6x+lambda=0 and 3 alpha+2 beta=-20 ,then lambda=

If alpha, beta are the roots of equation 3x^(2)-4x+2=0 , then the value of (alpha)/(beta)+(beta)/(alpha) 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: